Cheers, 49 NEW PRENUMBERED sequences, A091202-A091215, A091219-A091233, A091238-A091257 follow:

I have given the epiteth "nice" to A091204 & A091205 by myself,
as I think they deserve it. Probably they could have better names,
though.
Additions to index entries follow in a separate mail,
as well as the Scheme-program GF2Xfuns.scm.txt


%I A091202
%S A091202 0,1,2,3,4,7,6,11,8,5,14,13,12,19,22,9,16,25,10,31,28,29,26,37,24,21,
%T A091202 38,15,44,41,18,47,32,23,50,49,20,55,62,53,56,59,58,61,52,27,74,67,48,
%U A091202 69,42,43,76,73,30,35,88,33,82,87,36,91,94,39,64,121,46,97,100,111,98
%N A091202 Factorization-preserving isomorphism from integers to GF(2)[X]-polynomials.
%F A091202 a(0)=0, a(1)=1, a(p_i) = A014580(i) for primes with index i, and for composites a(p_i * p_j * ...) = a(p_i) X a(p_j) X ..., where X stands for carryless multiplication of two GF(2)[X] polynomials (A048720).
%C A091202 E.g. we have the following identities: A000005(n) = A091220(a(n)), A001221(n) = A091221(a(n)), A001222(n) = A091222(a(n)), A008683(n) = A091219(a(n)), A014580(n) = a(A000040(n)), A049084(n) = A091227(a(n)).
%H A091202 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091202 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A091202 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%Y A091202 Inverse: A091203. Cf. A091204 for "deep" variant.
%K A091202 nonn
%O A091202 0,3
%A A091202 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091203
%S A091203 0,1,2,3,4,9,6,5,8,15,18,7,12,11,10,27,16,81,30,13,36,25,14,33,24,17,
%T A091203 22,45,20,21,54,19,32,57,162,55,60,23,26,63,72,29,50,51,28,135,66,31,
%U A091203 48,35,34,243,44,39,90,37,40,99,42,41,108,43,38,75,64,225,114,47,324
%N A091203 Factorization-preserving isomorphism from GF(2)[X]-polynomials to integers.
%F A091203 a(0)=0, a(1)=1. For n's coding an irreducible polynomial, that is if n=A014580(i), we have a(n) = A000040(i), and for composite polynomials a(ir_i X ir_j X ...) = a(p_i) * a(p_j) * ..., where X stands for carryless multiplication of two GF(2)[X] polynomials (A048720), and * for the ordinary multiplication of integers (A004247).
%C A091203 E.g. we have the following identities: A000040(n) = a(A014580(n)), A091219(n) = A008683(a(n)), A091220(n) = A000005(a(n)), A091221(n) = A001221(a(n)), A091222(n) = A001222(a(n)), A091225(n) = A010051(a(n)), A091227(n) = A049084(a(n)), A091247(n) = A066247(a(n)).
%H A091203 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091203 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A091203 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%Y A091203 Inverse: A091202. Cf. A091205 for "deep" variant.
%K A091203 nonn
%O A091203 0,3
%A A091203 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091204
%S A091204 0,1,2,3,4,7,6,11,8,5,14,25,12,19,22,9,16,47,10,31,28,29,50,13,24,21,
%T A091204 38,15,44,61,18,137,32,43,94,49,20,55,62,53,56,97,58,115,100,27,26,37,
%U A091204 48,69,42,113,76,73,30,79,88,33,122,319,36,41,274,39,64,121,86,185
%N A091204 Deep multiplicative isomorphism from integers to GF(2)[X]-polynomials.
%F A091204 a(0)=0, a(1)=1, a(p_i) = A014580(a(i)) for primes with index i, and for composites a(p_i * p_j * ...) = a(p_i) X a(p_j) X ..., where X stands for carryless multiplication of two GF(2)[X] polynomials (A048720).
%C A091204 This isomorphism can be used in most cases where mere A091202 would work, but in addition this preserves also the structures where we recurse on prime's index. E.g. we have: A091230(n) = a(A007097(n)) and A061775(n) = A091238(a(n)). This is possible because the permutation contains an image of itself in its restriction to primes, i.e. a(n) = A091227(a(A000040(n))).
%H A091204 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091204 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A091204 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%Y A091204 Inverse: A091205.
%K A091204 nonn,nice
%O A091204 0,3
%A A091204 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091205
%S A091205 0,1,2,3,4,9,6,5,8,15,18,7,12,23,10,27,16,81,30,13,36,25,14,69,24,11,
%T A091205 46,45,20,21,54,19,32,57,162,115,60,47,26,63,72,61,50,33,28,135,138,
%U A091205 17,48,35,22,243,92,39,90,37,40,207,42,83,108,29,38,75,64,225,114,103
%N A091205 Deep multiplicative isomorphism from GF(2)[X]-polynomials to integers.
%F A091205 a(0)=0, a(1)=1. For n's coding an irreducible polynomial, that is if n=A014580(i), we have a(n) = A000040(a(i)), and for reducible polynomials a(ir_i X ir_j X ...) = a(p_i) * a(p_j) * ..., where X stands for carryless multiplication of two GF(2)[X] polynomials (A048720), and * for the ordinary multiplication of integers (A004247).
%C A091205 This isomorphism can be used in most cases where mere A091203 would work, but in addition this preserves also the structures where we recurse on irreducible polynomial's A014580-index. E.g. we have: A091238(n) = A061775(a(n)). This is possible because the permutation contains an image of itself in its restriction to irreducible polynomials, i.e. a(n) = A049084(a(A014580(n))).
%H A091205 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091205 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A091205 <a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%Y A091205 Inverse: A091204.
%K A091205 nonn,nice
%O A091205 0,3
%A A091205 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091206
%S A091206 2,3,7,11,13,19,31,37,41,47,59,61,67,73,97,103,109,131,137,157,167,
%T A091206 191,193,211,229,239,241,283,313,379,397,419,433,463,487,499,557,563,
%U A091206 587,601,607,613,617,631,647,661,677,701,719,757,761,769,787,827,859
%N A091206 Primes that are also irreducible GF(2)[X]-polynomials.
%H A091206 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091206 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091206 a(n) = A000040(A091207(n)) = A014580(A091208(n)). Intersect of A014580 & A000040. Apart from a(2)=3 a subset of A027697.
%K A091206 nonn
%O A091206 1,1
%A A091206 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091207
%S A091207 1,2,4,5,6,8,11,12,13,15,17,18,19,21,25,27,29,32,33,37,39,43,44,47,50,
%T A091207 52,53,61,65,75,78,81,84,90,93,95,102,103,107,110,111,112,113,115,118,
%U A091207 121,123,126,128,134,135,136,138,144,149,151,153,156,158,162,163,164
%N A091207 Indices of primes that are also irreducible GF(2)[X]-polynomials.
%H A091207 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%Y A091207 a(n) = A049084(A091206(n)). Complement of A091210.
%K A091207 nonn
%O A091207 1,2
%A A091207 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091208
%S A091208 1,2,3,4,5,6,8,9,10,11,13,14,15,16,19,20,21,24,25,28,29,32,33,35,37,
%T A091208 38,39,42,46,55,58,60,62,65,68,69,77,78,79,80,81,82,83,85,87,88,91,94,
%U A091208 95,98,99,100,101,106,109,112,113,116,117,119,120,121,127,128,129,130
%N A091208 A014580-indices of irreducible GF(2)[X]-polynomials that are also primes.
%H A091208 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%Y A091208 a(n) = A091227(A091206(n)). Complement of A091215.
%K A091208 nonn
%O A091208 1,2
%A A091208 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091209
%S A091209 5,17,23,29,43,53,71,79,83,89,101,107,113,127,139,149,151,163,173,179,
%T A091209 181,197,199,223,227,233,251,257,263,269,271,277,281,293,307,311,317,
%U A091209 331,337,347,349,353,359,367,373,383,389,401,409,421,431,439,443,449
%N A091209 Primes that are composite GF(2)[X]-polynomials.
%H A091209 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091209 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091209 a(n) = A000040(A091210(n)) = A091242(A091211(n)). Intersect of A000040 and A091242.
%K A091209 nonn
%O A091209 1,1
%A A091209 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091210
%S A091210 3,7,9,10,14,16,20,22,23,24,26,28,30,31,34,35,36,38,40,41,42,45,46,48,
%T A091210 49,51,54,55,56,57,58,59,60,62,63,64,66,67,68,69,70,71,72,73,74,76,77,
%U A091210 79,80,82,83,85,86,87,88,89,91,92,94,96,97,98,99,100,101,104,105,106
%N A091210 Indices of primes that are composite GF(2)[X]-polynomials.
%H A091210 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091210 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091210 a(n) = A049084(A091209(n)). Complement of A091207.
%K A091210 nonn
%O A091210 1,1
%A A091210 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091211
%S A091211 2,11,16,21,32,41,55,62,66,71,81,86,91,103,113,121,123,134,142,148,
%T A091211 150,163,165,186,190,195,210,215,221,227,229,235,239,249,261,265,270,
%U A091211 283,288,298,300,303,307,314,319,327,333,342,350,360,369,376,380,385
%N A091211 A091242-indices of primes that are composite GF(2)[X]-polynomials.
%H A091211 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091211 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091211 a(n) = A091246(A091209(n)). Complement of A091213.
%K A091211 nonn
%O A091211 1,1
%A A091211 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091212
%S A091212 4,6,8,9,10,12,14,15,16,18,20,21,22,24,26,27,28,30,32,33,34,35,36,38,
%T A091212 39,40,42,44,45,46,48,49,50,51,52,54,56,57,58,60,62,63,64,65,66,68,69,
%U A091212 70,72,74,75,76,77,78,80,81,82,84,85,86,88,90,92,93,94,95,96,98,99
%N A091212 Composite GF(2)[X]-polynomials that are also composite integers.
%H A091212 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091212 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091212 a(n) = A091242(A091213(n)). Intersect of A002808 and A091242.
%K A091212 nonn
%O A091212 1,1
%A A091212 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091213
%S A091213 1,3,4,5,6,7,8,9,10,12,13,14,15,17,18,19,20,22,23,24,25,26,27,28,29,
%T A091213 30,31,33,34,35,36,37,38,39,40,42,43,44,45,46,47,48,49,50,51,52,53,54,
%U A091213 56,57,58,59,60,61,63,64,65,67,68,69,70,72,73,74,75,76,77,78,79,80,82
%N A091213 A091242-indices of composite GF(2)[X]-polynomials that are also composite integers.
%H A091213 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091213 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091213 a(n) = A091246(A091212(n)). Complement of A091211.
%K A091213 nonn
%O A091213 1,2
%A A091213 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091214
%S A091214 25,55,87,91,115,117,143,145,171,185,203,213,247,253,285,299,301,319,
%T A091214 333,351,355,357,361,369,375,391,395,415,425,445,451,471,477,501,505,
%U A091214 515,529,535,539,545,623,637,665,675,687,695,721,731,789,799,803,817
%N A091214 Irreducible GF(2)[X]-polynomials that are composite integers.
%H A091214 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091214 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091214 a(n) = A014580(A091215(n)). Intersect of A002808 and A014580.
%K A091214 nonn
%O A091214 1,1
%A A091214 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091215
%S A091215 7,12,17,18,22,23,26,27,30,31,34,36,40,41,43,44,45,47,48,49,50,51,52,
%T A091215 53,54,56,57,59,61,63,64,66,67,70,71,72,73,74,75,76,84,86,89,90,92,93,
%U A091215 96,97,102,103,104,105,107,108,110,111,114,115,118,122,123,124,125
%N A091215 A014580-indices of irreducible GF(2)[X]-polynomials that are composite integers.
%H A091215 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%Y A091215 a(n) = A091227(A091214(n)). Complement of A091208.
%K A091215 nonn
%O A091215 1,1
%A A091215 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091219
%S A091219 1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,
%T A091219 1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,
%U A091219 1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0
%V A091219 1,-1,-1,0,0,1,-1,0,1,0,-1,0,-1,1,0,0,0,-1,-1,0,0,1,1,0,-1,1,0,0,1,0,
%W A091219 -1,0,1,0,1,0,-1,1,0,0,-1,0,1,0,0,-1,-1,0,1,1,0,0,1,0,-1,0,0,-1,-1,0,
%X A091219 -1,1,0,0,0,-1,-1,0,0,-1,1,0,-1,1,0,0,1,0,1,0,0,1,-1,0,0,-1,-1,0,1,0
%N A091219 Moebius-analog for the domain GF(2)[X]: a(n)=0 if A091221(n)!=A091222(n) (i.e. if the polynomial is not square-free), otherwise (-1)^A091222(n).
%C A091219 The absolute values give a characteristic function for square-free GF(2)[X]-polynomials.
%H A091219 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091219 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091219 a(n) = A008683(A091203(n)) = A008683(A091205(n)).
%K A091219 sign
%O A091219 1,1
%A A091219 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004


%I A091220
%S A091220 1,2,2,3,3,4,2,4,4,6,2,6,2,4,4,5,5,8,2,9,3,4,4,8,2,4,6,6,4,8,2,6,4,10,
%T A091220 4,12,2,4,6,12,2,6,4,6,8,8,2,10,4,4,6,6,4,12,2,8,6,8,2,12,2,4,6,7,9,8,
%U A091220 2,15,3,8,4,16,2,4,8,6,4,12,4,15,3,4,8,9,7,8,2,8,4,16,2,12,4,4,6,12,2
%N A091220 Number of divisors in the nth GF(2)[X]-polynomial.
%H A091220 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091220 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091220 a(n) = A000005(A091203(n)) = A000005(A091205(n)). Cf. A091257.
%K A091220 nonn
%O A091220 1,2
%A A091220 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091221
%S A091221 0,1,1,1,1,2,1,1,2,2,1,2,1,2,1,1,1,3,1,2,1,2,2,2,1,2,2,2,2,2,1,1,2,2,
%T A091221 2,3,1,2,2,2,1,2,2,2,2,3,1,2,2,2,1,2,2,3,1,2,2,3,1,2,1,2,2,1,2,3,1,2,
%U A091221 1,3,2,3,1,2,2,2,2,3,2,2,1,2,3,2,1,3,1,2,2,3,1,3,2,2,2,2,1,3,2,2,3,2
%N A091221 Number of distinct irreducible polynomials dividing nth GF(2)[X]-polynomial.
%H A091221 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091221 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091221 a(n) = A001221(A091203(n)) = A001221(A091205(n)). A000374(n) = a(A000051(n)).
%K A091221 nonn
%O A091221 1,6
%A A091221 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091222
%S A091222 0,1,1,2,2,2,1,3,2,3,1,3,1,2,3,4,4,3,1,4,2,2,2,4,1,2,3,3,2,4,1,5,2,5,
%T A091222 2,4,1,2,3,5,1,3,2,3,4,3,1,5,2,2,5,3,2,4,1,4,3,3,1,5,1,2,3,6,4,3,1,6,
%U A091222 2,3,2,5,1,2,4,3,2,4,2,6,2,2,3,4,6,3,1,4,2,5,1,4,2,2,3,6,1,3,3,3,3,6
%N A091222 Number of irreducible polynomials dividing nth GF(2)[X]-polynomial, counted with multiplicity.
%H A091222 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091222 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091222 a(n) = A001222(A091203(n)) = A001222(A091205(n)). A091248(n) = a(A000051(n)).
%K A091222 nonn
%O A091222 1,4
%A A091222 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091223
%S A091223 1,4,4,2,6,6,6,6,4,6,8,4,2,6,6,14,4,6,6,6,6,2,14,6,6,2,12,10,4,14,6,2,
%T A091223 10,8,2,16,10,2,6,6,30,2,14,2,12,6,14,18,4,2,4,8,6,4,12,4,2,18,4,6,8,
%U A091223 12,6,12,8,6,10,12,2,4,10,14,6,4,6,12,6,24,14,6,6,4,6,8,6,10,14,4,10
%N A091223 Differences between consecutive irreducible GF(2)[X]-polynomials.
%C A091223 Analogous to A001223.
%H A091223 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091223 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091223 First differences of A014580. Divided by 2: A091224.
%K A091223 nonn
%O A091223 1,2
%A A091223 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091224
%S A091224 2,2,1,3,3,3,3,2,3,4,2,1,3,3,7,2,3,3,3,3,1,7,3,3,1,6,5,2,7,3,1,5,4,1,
%T A091224 8,5,1,3,3,15,1,7,1,6,3,7,9,2,1,2,4,3,2,6,2,1,9,2,3,4,6,3,6,4,3,5,6,1,
%U A091224 2,5,7,3,2,3,6,3,12,7,3,3,2,3,4,3,5,7,2,5,1,5,4,3,9,1,5,13,2,4,9,1,5
%N A091224 Differences between consecutive irreducible GF(2)[X]-polynomials, divided by 2.
%C A091224 Analogous to A028334.
%H A091224 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%Y A091224 a(n) = A091223(n)/2.
%K A091224 nonn
%O A091224 2,1
%A A091224 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091225
%S A091225 0,0,1,1,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,
%T A091225 0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,
%U A091225 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0
%N A091225 Characteristic function of A014580: 1 if the nth GF(2)[X] polynomial is irreducible, 0 otherwise.
%H A091225 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091225 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091225 a(n) = A010051(A091203(n)) = A010051(A091205(n)). Partial sums give A091226. Cf. A091227. Complementary to A091247.
%K A091225 nonn
%O A091225 0,1
%A A091225 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091226
%S A091226 0,0,1,2,2,2,2,3,3,3,3,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,
%T A091226 8,8,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,12,12,12,12,
%U A091226 13,13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16
%N A091226 Number of irreducible GF(2)[X]-polynomials in range [0,n].
%C A091226 Analogous to A000720.
%H A091226 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091226 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091226 Partial sums of A091225. A062692(n) = a(2^n).
%K A091226 nonn
%O A091226 0,4
%A A091226 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091227
%S A091227 0,1,2,0,0,0,3,0,0,0,4,0,5,0,0,0,0,0,6,0,0,0,0,0,7,0,0,0,0,0,8,0,0,0,
%T A091227 0,0,9,0,0,0,10,0,0,0,0,0,11,0,0,0,0,0,0,0,12,0,0,0,13,0,14,0,0,0,0,0,
%U A091227 15,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,0,0,0,0,17,0,0,0,18,0,0,0,0,0,19,0
%N A091227 Inverse function of A014580: position in A014580 if the nth GF(2)[X] polynomial is irreducible, 0 otherwise.
%F A091227 a(n) = A091225(n) * A091226(n).
%H A091227 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091227 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091227 Inverse of A014580. a(n) = A049084(A091203(n)).
%K A091227 nonn
%O A091227 1,3
%A A091227 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091228
%S A091228 2,2,2,3,7,7,7,7,11,11,11,11,13,13,19,19,19,19,19,19,25,25,25,25,25,
%T A091228 25,31,31,31,31,31,31,37,37,37,37,37,37,41,41,41,41,47,47,47,47,47,47,
%U A091228 55,55,55,55,55,55,55,55,59,59,59,59,61,61,67,67,67,67,67,67,73,73,73
%N A091228 Smallest m >= n, such that m is irreducible when interpreted as GF(2)[X]-polynomial.
%F A091228 a(n) = n + A091229(n).
%C A091228 Analogous to A007918.
%H A091228 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091228 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%K A091228 nonn
%O A091228 0,1
%A A091228 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091229
%S A091229 2,1,0,0,3,2,1,0,3,2,1,0,1,0,5,4,3,2,1,0,5,4,3,2,1,0,5,4,3,2,1,0,5,4,
%T A091229 3,2,1,0,3,2,1,0,5,4,3,2,1,0,7,6,5,4,3,2,1,0,3,2,1,0,1,0,5,4,3,2,1,0,
%U A091229 5,4,3,2,1,0,13,12,11,10,9,8,7,6,5,4,3,2,1,0,3,2,1,0,5,4,3,2,1,0,5,4
%N A091229 Smallest k such that n+k is irreducible when interpreted as GF(2)[X]-polynomial.
%F A091229 a(n) = A091228(n) - n.
%C A091229 Analogous to A007920.
%H A091229 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091229 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%K A091229 nonn
%O A091229 0,1
%A A091229 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091230
%S A091230 1,2,3,7,25,137,1123,13103
%N A091230 Iterates of A014580.
%F A091230 a(0)=1, a(n) = A014580(a(n-1)).
%H A091230 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091230 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091230 a(n) = A091204(A007097(n)). A091238(a(n)) = n+1.
%K A091230 nonn
%O A091230 0,2
%A A091230 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091231
%S A091231 0,0,0,1,1,3,4,8,13,26,45,83,152,281,523,974,1822,3451,6490,12348,
%T A091231 23389,44598,85076,162735,311721,598669,1150613,2215562,4271844,
%U A091231 8247356,15941844,30849114,59758104,115878009,224900328
%N A091231 How many more primes than irreducible GF(2)[X] polynomials there are in range [0,2^n].
%F A091231 a(0)=a(1)=0, a(n) = A007053(n)-A062692(n-1).
%e A091231 There are 11 primes (2,3,5,7,11,13,17,19,23,29,31) in range [0,32], while there are only 8 irreducible GF(2)[X]-polynomials in the same range: (2,3,7,11,13,19,25,31), thus a(5)=3.
%H A091231 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091231 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091231 Partial sums of A091232.
%K A091231 nonn
%O A091231 0,6
%A A091231 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091232
%S A091232 0,0,1,0,2,1,4,5,13,19,38,69,129,242,451,848,1629,3039,5858,11041,
%T A091232 21209,40478,77659,148986,286948,551944,1064949,2056282,3975512,
%U A091232 7694488,14907270,28908990,56119905,109022319,211980753
%N A091232 How many more primes than irreducible GF(2)[X] polynomials there are in range [2^n,2^(n+1)].
%F A091232 a(0)=a(1)=0, a(n) = A036378(n+1)-A001037(n).
%e A091232 There are 5 primes (17,19,23,29,31) in range [16,32], while there are only 3 irreducible GF(2)[X]-polynomials in the same range: (19,25,31), thus a(4)=2.
%H A091232 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091232 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091232 First differences of A091231.
%K A091232 nonn
%O A091232 0,5
%A A091232 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091233
%S A091233 1,1,2,4,11,53,307,2177,19503,219489,3041937,50727755,997525229,
%T A091233 22742733167,592821131015,17461204518199
%N A091233 Size of range [Smallest Matula number coding a tree of n nodes,Largest Matula number coding a tree of n nodes].
%F A091233 a(n) = (A005518(n)-A005517(n))+1.
%H A091233 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%Y A091233 Compare to A091241 and A000081. Cf. A061773.
%K A091233 nonn
%O A091233 1,3
%A A091233 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091238
%S A091238 1,2,3,3,5,4,4,4,6,6,4,5,6,5,7,5,9,7,5,7,7,5,8,6,5,7,8,6,6,8,5,6,7,10,
%T A091238 9,8,7,6,8,8,7,8,7,6,10,9,5,7,7,6,11,8,7,9,6,7,10,7,7,9,6,6,9,7,11,8,
%U A091238 8,11,7,10,8,9,6,8,12,7,9,9,8,9,11,8,9,9,13,8,10,7,8,11,8,10,8,6,9,8
%N A091238 Number of nodes in rooted tree with GF2X-Matula number n.
%C A091238 Each n occurs A000081(n) times.
%e A091238 GF2X-Matula numbers for unoriented rooted trees are constructed otherwise just like the standard Matula-Goebel numbers (cf. A061773), but instead of normal factorization in N, one factorizes in polynomial ring GF(2)[X] as follows. Here IR(n) is the nth irreducible polynomial (A014580(n)), and X stands for GF(2)[X]-multiplication (A048720):
%e A091238 ................................................o...................o
%e A091238 ................................................|...................|
%e A091238 ............o...............o...o........o......o...............o...o
%e A091238 ............|...............|...|........|......|...............|...|
%e A091238 ...o........o......o...o....o...o....o...o......o......o.o.o....o...o
%e A091238 ...|........|.......\./......\./......\./.......|.......\|/......\./.
%e A091238 x..x........x........x........x........x........x........x........x..
%e A091238 1..2=IR(1)..3=IR(2)..4=2X2....5=3X3....6=2x3....7=IR(3)..8=2X2X2..9=3X7
%e A091238 Counting the vertices (marked with x's and o's) of each tree above, we get the eight initial terms of this sequence: 1,2,3,3,5,4,4,4,6.
%H A091238 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091238 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091238 a(n) = A061775(A091205(n)). a(A091230(n)) = n+1. Cf. A091239-A091241.
%K A091238 nonn
%O A091238 1,2
%A A091238 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091239
%S A091239 1,2,3,6,5,9,15,23,17,34,51,75,85,153,255,359,257,514,771,1275,1285,
%T A091239 2313,3855,5911,4369,8738,13107,19275,21845,39321,65535
%N A091239 Smallest GF2X-Matula number i which encodes a tree of n nodes, i.e. for which A091238(i) = n.
%H A091239 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%Y A091239 Analogous to A005517. A091240 gives the largest i with number of nodes = n. Cf. A091238, A091241.
%K A091239 nonn
%O A091239 1,2
%A A091239 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091240
%S A091240 1,2,4,11,47,319,3053,40345
%N A091240 Largest GF2X-Matula number i which encodes a tree of n nodes, i.e. for which A091238(i) = n.
%C A091240 Apparently from n=4 onward given by recurrence a(4)=A014580(4), a(5)=A014580(A014580(4)), a(6)=A014580(A014580(A014580(4))), etc.
%H A091240 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%Y A091240 Analogous to A005518. A091239 gives the smallest i with number of nodes = n. Cf. A091230, A091238, A091241.
%K A091240 nonn
%O A091240 1,2
%A A091240 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091241
%S A091241 1,1,2,6,43,311,3039,40323
%N A091241 Size of range [Smallest GF2X-Matula number coding a tree of n nodes,Largest GF2X-Matula number coding a tree of n nodes].
%F A091241 a(n) = (A091240(n)-A091239(n))+1.
%H A091241 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%Y A091241 Compare to A091233 and A000081.
%K A091241 nonn
%O A091241 1,3
%A A091241 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091242
%S A091242 4,5,6,8,9,10,12,14,15,16,17,18,20,21,22,23,24,26,27,28,29,30,32,33,
%T A091242 34,35,36,38,39,40,42,43,44,45,46,48,49,50,51,52,53,54,56,57,58,60,62,
%U A091242 63,64,65,66,68,69,70,71,72,74,75,76,77,78,79,80,81,82,83,84,85,86,88
%N A091242 Reducible GF(2)[X]-polynomials.
%C A091242 Analogous to A002808.
%e A091242 For example, 5 = 101 in binary encodes the polynomial x^2+1 which is factored as (x+1)^2 in the polynomial ring GF(2)[X].
%H A091242 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091242 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091242 Inverse: A091246. Almost complement of A014580. Union of A091209 & A091212. First differences: A091243. Characteristic function: A091247. In binary format: A091254.
%K A091242 nonn
%O A091242 1,1
%A A091242 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091243
%S A091243 1,1,2,1,1,2,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,2,1,1,1,1,
%T A091243 2,1,1,1,1,1,1,2,1,1,2,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,
%U A091243 2,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1
%N A091243 Differences between consecutive reducible GF(2)[X]-polynomials.
%C A091243 Analogous to A073783.
%H A091243 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091243 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091243 First differences of A091242. a(n) = A091244(n)+1.
%K A091243 nonn
%O A091243 1,3
%A A091243 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091244
%S A091244 0,0,1,0,0,1,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,
%T A091244 1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%U A091244 1,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0
%N A091244 Number of irreducible polynomials between successive reducible GF(2)[X]-polynomials.
%C A091244 Analogous to A073784.
%H A091244 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091244 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091244 A091243(n)-1.
%K A091244 nonn
%O A091244 1,1
%A A091244 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091245
%S A091245 0,0,0,0,1,2,3,3,4,5,6,6,7,7,8,9,10,11,12,12,13,14,15,16,17,17,18,19,
%T A091245 20,21,22,22,23,24,25,26,27,27,28,29,30,30,31,32,33,34,35,35,36,37,38,
%U A091245 39,40,41,42,42,43,44,45,45,46,46,47,48,49,50,51,51,52,53,54,55,56,56
%N A091245 Number of reducible GF(2)[X]-polynomials in range [0,n].
%C A091245 Analogous to A065855.
%e A091245 In range [0,8] there are the following four reducible polynomials: 4,5,6,8 thus a(8) = 4.
%H A091245 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091245 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091245 Partial sums of A091247. Cf. A091242.
%K A091245 nonn
%O A091245 0,6
%A A091245 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091246
%S A091246 0,0,0,1,2,3,0,4,5,6,0,7,0,8,9,10,11,12,0,13,14,15,16,17,0,18,19,20,
%T A091246 21,22,0,23,24,25,26,27,0,28,29,30,0,31,32,33,34,35,0,36,37,38,39,40,
%U A091246 41,42,0,43,44,45,0,46,0,47,48,49,50,51,0,52,53,54,55,56,0,57,58,59
%N A091246 Inverse function of A091242: position in A091242 if the nth GF(2)[X] polynomial is reducible, 0 otherwise.
%F A091246 a(n) = A091245(n) * A091247(n).
%C A091246 Analogous to A066246.
%H A091246 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091246 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091246 Inverse of A091242.
%K A091246 nonn
%O A091246 1,5
%A A091246 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091247
%S A091247 0,0,0,0,1,1,1,0,1,1,1,0,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,
%T A091247 1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,0,1,0,1,1,1,1,1,0,
%U A091247 1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1
%N A091247 Characteristic function of A091242: 1 if the nth GF(2)[X] polynomial is reducible, 0 otherwise.
%H A091247 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091247 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091247 a(n) = A066247(A091203(n)) = A066247(A091205(n)). Complementary to A091225. Partial sums give A091245. Cf. A091246
%K A091247 nonn
%O A091247 0,1
%A A091247 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091248
%S A091248 1,2,2,4,2,4,3,8,3,4,2,8,2,6,5,16,3,6,2,8,6,4,3,16,3,4,4,12,2,10,7,32,
%T A091248 5,6,6,12,2,4,5,16,3,12,4,8,8,6,3,32,5,6,8,8,2,8,5,24,5,4,2,20,2,14,
%U A091248 13,64,7,10,2,12,6,12,3,24,9,4,8,8,6,10,3,32,5,6,2,24,12,8,5,16,9,16
%N A091248 Number of irreducible factors in the factorization of GF(2)[X]-polynomial x^n+1 (counted with multiplicity).
%F A091248 a(n) = A091222(A000051(n)).
%H A091248 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091248 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%K A091248 nonn
%Y A091248 A000374 gives the number of distinct irreducible factors of the same polynomials.
%O A091248 1,2
%A A091248 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091249
%S A091249 2,3,4,5,6,7,9,10,11,12,13,14,15,18,19,20,21,22,24,25,26,27,28,29,30,
%T A091249 31,32,33,34,35,36,37,38,39,40,41,43,44,45,48,49,50,51,52,53,56,58,61,
%U A091249 64,65,68,70,73,75,76,77,78,80,81,83,84,85,86,87,88,90,91,92,93,94,95
%N A091249 A014580-indices of primitive irreducible GF(2)[X]-polynomials.
%H A091249 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091249 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091249 a(n) = A091227(A091250(n)). Complement of A091251.
%K A091249 nonn
%O A091249 1,1
%A A091249 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091250
%S A091250 3,7,11,13,19,25,37,41,47,55,59,61,67,91,97,103,109,115,131,137,143,
%T A091250 145,157,167,171,185,191,193,203,211,213,229,239,241,247,253,285,299,
%U A091250 301,333,351,355,357,361,369,391,397,425,451,463,487,501,529,539,545
%N A091250 Primitive irreducible polynomials over GF(2).
%H A091250 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091250 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091250 a(n) = A014580(A091249(n)). Cf. A011260, A091252. A007088(a(n)) = A058947(n) (same sequence in binary).
%K A091250 nonn
%O A091250 1,1
%A A091250 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091251
%S A091251 1,8,16,17,23,42,46,47,54,55,57,59,60,62,63,66,67,69,71,72,74,79,82,
%T A091251 89,100,107,117
%N A091251 A014580-indices of non-primitive irreducible GF(2)[X]-polynomials.
%H A091251 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091251 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091251 a(n) = A091227(A091252(n)). Complement of A091249.
%K A091251 nonn
%O A091251 1,2
%A A091251 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091252
%S A091252 2,31,73,87,117,283,313,319,375,379,395,415,419,433,445,471,477,499,
%T A091252 505,515,535,587,613,665,769,841,929
%N A091252 Non-primitive irreducible polynomials over GF(2).
%H A091252 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091252 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091252 a(n) = A014580(A091251(n)). Cf. A091250. In binary format: A091253.
%K A091252 nonn
%O A091252 1,1
%A A091252 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091253
%S A091253 10,11111,1001001,1010111,1110101,100011011,100111001,100111111,
%T A091253 101110111,101111011,110001011,110011111,110100011,110110001,
%U A091253 110111101,111010111,111011101,111110011,111111001,1000000011
%N A091253 Non-primitive irreducible polynomials over GF(2), in binary format.
%H A091253 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091253 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091253 a(n) = A007088(A091252(n)).
%K A091253 nonn
%O A091253 1,1
%A A091253 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091254
%S A091254 100,101,110,1000,1001,1010,1100,1110,1111,10000,10001,10010,10100,
%T A091254 10101,10110,10111,11000,11010,11011,11100,11101,11110,100000,100001,
%U A091254 100010,100011,100100,100110,100111,101000,101010,101011,101100
%N A091254 Reducible polynomials over GF(2), in binary format.
%H A091254 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091254 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091254 a(n) = A007088(A091242(n)). Cf. A058943.
%K A091254 nonn
%O A091254 1,1
%A A091254 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091255
%S A091255 1,1,1,1,2,1,1,1,1,1,1,2,3,2,1,1,1,1,1,1,1,1,2,3,4,3,2,1,1,1,3,1,1,3,
%T A091255 1,1,1,2,1,2,5,2,1,2,1,1,1,1,1,3,3,1,1,1,1,1,2,3,4,1,6,1,4,3,2,1,1,1,
%U A091255 3,1,1,1,1,1,1,3,1,1,1,2,1,2,3,2,7,2,3,2,1,2,1,1,1,3,1,5,3,1,1,3,5,1
%N A091255 Table of GCD(x,y) computed for polynomials over GF(2), where (x,y) runs as (1,1),(1,2),(2,1),(1,3),(2,2),(3,1),...
%C A091255 Analogous to A003989.
%H A091255 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091255 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A091255 <A HREF="http://www.research.att.com/~njas/sequences/Sindx_La.html#Lattices">Index entries for sequences related to Lattices</A>
%Y A091255 Cf. A091256, A091257.
%K A091255 nonn,tabl
%O A091255 1,5
%A A091255 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091256
%S A091256 1,2,2,3,2,3,4,6,6,4,5,4,3,4,5,6,10,12,12,10,6,7,6,5,4,5,6,7,8,14,6,
%T A091256 20,20,6,14,8,9,8,9,12,5,12,9,8,9,10,18,24,28,10,10,28,24,18,10,11,10,
%U A091256 9,8,27,6,27,8,9,10,11,12,22,10,36,40,18,18,40,36,10,22,12,13,12,29
%N A091256 Table of LCM(x,y) computed for polynomials over GF(2), where (x,y) runs as (1,1),(1,2),(2,1),(1,3),(2,2),(3,1),...
%C A091256 Analogous to A003990.
%H A091256 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091256 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A091256 <A HREF="http://www.research.att.com/~njas/sequences/Sindx_La.html#Lattices">Index entries for sequences related to Lattices</A>
%Y A091256 Cf. A091255, A091257.
%K A091256 nonn,tabl
%O A091256 1,2
%A A091256 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

%I A091257
%S A091257 1,2,2,3,4,3,4,6,6,4,5,8,5,8,5,6,10,12,12,10,6,7,12,15,16,15,12,7,8,
%T A091257 14,10,20,20,10,14,8,9,16,9,24,17,24,9,16,9,10,18,24,28,30,30,28,24,
%U A091257 18,10,11,20,27,32,27,20,27,32,27,20,11,12,22,30,36,40,18,18,40,36,30
%N A091257 Multiplication table A x B computed for polynomials over GF(2), where (A,B) runs as (1,1),(1,2),(2,1),(1,3),(2,2),(3,1),...
%C A091257 Essentially same as A048720 but computed starting from offset one instead of zero. Analogous to A003991. Each n occurs A091220(n) times.
%H A091257 A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/GF2Xfuns.scm.txt">Scheme-program for computing this sequence.</a>
%H A091257 <a href="http://www.research.att.com/~njas/sequences/Sindx_Ge.html#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%Y A091257 a(n) = A048720bi(A091255(n),A091256(n)), because the identity A x B = GCD(A,B) x LCM(A,B) holds also in the polynomial ring GF(2)[X].
%K A091257 nonn,tabl
%O A091257 1,2
%A A091257 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004


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Yours,

Antti Karttunen