------------------------------------------------------------------------------

Additions to the index entry
http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation

paired with its inverse: (7) A073290-A073291, A073292-A073293, A073294-A073295, A073296-A073297, A073298-A073299


%I A074679
%S A074679 0,1,3,2,6,7,8,4,5,14,15,16,17,18,19,20,21,9,10,22,11,12,13,37,38,39,40,41,42,43,44,45,46,47,
%T A074679 48,49,50,51,52,53,54,55,56,57,58,23,24,59,25,26,27,60,61,62,28,29,63,30,31,32,64,33,34,35,
%U A074679 36,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128
%N A074679 Permutation of natural numbers induced by the gatomorphism gmRobl! acting on the parenthesizations encoded by A014486/A063171.
%R A074679
%H A074679 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(With the complete Scheme source)</I>
%H A074679 <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>
%O A074679 0,3
%K A074679 nonn
%A A074679 Antti Karttunen (my_firstname.my_surname@iki.fi) Aug 30 2002
%D A074679
%Y A074679 Inverse of A074680 and also a(n) = A057163(A074680(A057163(n))). Cf. A074681-A074690. The car/cdr-flipped conjugate of A074680, i.e. a(n) = A057163(A074680(A057163(n))). Occurs first time in A073200 as the row ???. Fixed point counts and cycle counts are given in ???
%o A074679 (Scheme function implementing this automorphism on list-structures:)
%o A074679 (define (gmRobl! s) (gmA072796! s) (SwapBinTree! s) (ReflectBinTree! s) (gmA072796! s) (ReflectBinTree! s) s)
%o A074679 (define (gmA072796! s) (cond ((not (pair? s)) s) ((not (pair? (cdr s))) s) (else (swap! s) (robr! s) (swap! (cdr s)) s)))
%o A074679 (define (robr! s) (let ((ex-cdr (cdr s))) (set-cdr! s (caar s)) (set-car! (car s) ex-cdr) (swap! (car s)) (swap! s) s))
%o A074679 (define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))






%I A074680
%S A074680 0,1,3,2,7,8,4,5,6,17,18,20,21,22,9,10,11,12,13,14,15,16,19,45,46,48,49,50,54,55,57,58,59,61,
%T A074680 62,63,64,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,47,51,52,53,56,
%U A074680 60,129,130,132,133,134,138,139,141,142,143,145,146,147,148,157,158,160,161,162,166,167,169
%N A074680 Permutation of natural numbers induced by the gatomorphism gmRobr! acting on the parenthesizations encoded by A014486/A063171.
%R A074680
%H A074680 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(With the complete Scheme source)</I>
%H A074680 <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>
%O A074680 0,3
%K A074680 nonn
%A A074680 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%D A074680
%Y A074680 Inverse of A074679 and also a(n) = A057163(A074679(A057163(n))). Cf. A074681-A074690. Occurs first time in A073200 as the row ???. Fixed point counts and cycle counts are given in ???
%o A074680 (Scheme function implementing this automorphism on list-structures:)
%o A074680 (define (gmRobr! s) (ReflectBinTree! s) (gmA072796! s) (ReflectBinTree! s) (SwapBinTree! s) (gmA072796! s) s)
%o A074680 (define (gmA072796! s) (cond ((not (pair? s)) s) ((not (pair? (cdr s))) s) (else (swap! s) (robr! s) (swap! (cdr s)) s)))
%o A074680 (define (robr! s) (let ((ex-cdr (cdr s))) (set-cdr! s (caar s)) (set-car! (car s) ex-cdr) (swap! (car s)) (swap! s) s))
%o A074680 (define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))



%I A074681
%S A074681 0,1,3,2,6,8,7,5,4,15,14,19,20,22,16,21,18,11,13,17,12,10,9,39,41,40,38,37,52,51,53,55,54,60,
%T A074681 61,62,64,43,42,56,57,63,47,59,48,29,28,50,33,34,36,44,58,49,30,35,46,32,25,27,45,31,26,24,
%U A074681 23,113,112,117,118,120,114,119,116,109,111,115,110,108,107,151,153,152,150,149,155,154,159
%N A074681 Permutation of natural numbers induced by the gatomorphism gmA074681! acting on the parenthesizations encoded by A014486/A063171.
%R A074681
%H A074681 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(With the complete Scheme source)</I>
%H A074681 <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>
%O A074681 0,3
%K A074681 nonn
%A A074681 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%D A074681
%Y A074681 Inverse of A074682. a(n) = A057163(A074684(A057163(n))). Cf. A074685, A074687, A074689. Occurs first time in A073200 as the row ???.
%o A074681 (Scheme function implementing this automorphism on list-structures:)
%o A074681 (define (gmA074681! s) (cond ((pair? s) (gmrobl! s) (gmA074681! (car s)) (gmA074681! (cdr s)))) s)



%I A074682
%S A074682 0,1,3,2,8,7,4,6,5,22,21,17,20,18,10,9,14,19,16,11,12,15,13,64,63,58,62,59,46,45,54,61,57,48,
%T A074682 49,55,50,27,26,23,25,24,38,37,51,60,56,42,44,53,47,29,28,30,32,31,39,40,52,43,33,34,35,41,
%U A074682 36,196,195,189,194,190,171,170,184,193,188,174,175,185,176,134,133,129,132,130,158,157,180
%N A074682 Permutation of natural numbers induced by the gatomorphism gmA074682! acting on the parenthesizations encoded by A014486/A063171.
%R A074682
%H A074682 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(With the complete Scheme source)</I>
%H A074682 <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>
%O A074682 0,3
%K A074682 nonn
%A A074682 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%D A074682
%Y A074682 Inverse of A074681. a(n) = A057163(A074683(A057163(n))). Occurs first time in A073200 as the row ???.
%o A074682 (Scheme function implementing this automorphism on list-structures:)
%o A074682 (define (gmA074682! s) (cond ((pair? s) (gmA074682! (car s)) (gmA074682! (cdr s)) (gmrobr! s))) s)





%I A074683
%S A074683 0,1,3,2,7,6,8,5,4,17,16,18,15,14,20,19,22,12,11,21,13,10,9,45,44,46,43,42,48,47,50,40,39,49,
%T A074683 41,38,37,54,53,55,52,51,61,60,63,31,30,62,32,29,28,57,56,64,34,33,59,36,26,25,58,35,27,24,
%U A074683 23,129,128,130,127,126,132,131,134,124,123,133,125,122,121,138,137,139,136,135,145,144,147
%N A074683 Permutation of natural numbers induced by the gatomorphism gmA074683! acting on the parenthesizations encoded by A014486/A063171.
%R A074683
%H A074683 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(With the complete Scheme source)</I>
%H A074683 <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>
%O A074683 0,3
%K A074683 nonn
%A A074683 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%D A074683
%Y A074683 Inverse of A074684. a(n) = A057163(A074682(A057163(n))). Occurs first time in A073200 as the row ???.
%o A074681 (Scheme function implementing this automorphism on list-structures:)
%o A074683 (define (gmA074683! s) (cond ((pair? s) (gmA074683! (car s)) (gmA074683! (cdr s)) (gmrobl! s))) s)




%I A074684
%S A074684 0,1,3,2,8,7,5,4,6,22,21,18,17,20,13,12,10,9,11,15,14,19,16,64,63,59,58,62,50,49,46,45,48,55,
%T A074684 54,61,57,36,35,32,31,34,27,26,24,23,25,29,28,33,30,41,40,38,37,39,52,51,60,56,43,42,47,44,
%U A074684 53,196,195,190,189,194,176,175,171,170,174,185,184,193,188,148,147,143,142,146,134,133,130
%N A074684 Permutation of natural numbers induced by the gatomorphism gmA074684! acting on the parenthesizations encoded by A014486/A063171.
%R A074684
%H A074684 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(With the complete Scheme source)</I>
%H A074684 <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>
%O A074684 0,3
%K A074684 nonn
%A A074684 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%D A074684
%Y A074684 Inverse of A074683. a(n) = A057163(A074681(A057163(n))). Occurs first time in A073200 as the row ???.
%o A074684 (Scheme function implementing this automorphism on list-structures:)
%o A074684 (define (gmA074684! s) (cond ((pair? s) (gmrobr! s) (gmA074684! (car s)) (gmA074684! (cdr s)))) s)



%I A074685
%S A074685 0,1,3,2,6,7,8,5,4,15,14,16,17,18,19,20,21,11,12,22,13,10,9,39,40,41,38,37,43,42,44,45,46,47,
%T A074685 48,49,50,52,51,53,54,55,56,57,58,29,28,59,30,31,32,60,61,62,33,34,63,35,25,26,64,36,27,24,
%U A074685 23,113,112,114,115,116,117,118,119,109,110,120,111,108,107,123,124,125,122,121,127,126,128
%N A074685 Permutation of natural numbers induced by the gatomorphism gmA074685! acting on the parenthesizations encoded by A014486/A063171.
%R A074685
%H A074685 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(With the complete Scheme source)</I>
%H A074685 <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>
%O A074685 0,3
%K A074685 nonn
%A A074685 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%D A074685
%Y A074685 Inverse of A074686. a(n) = A057163(A074689(A057163(n))). Occurs first time in A073200 as the row ???.
%o A074685 (Scheme function implementing this automorphism on list-structures:)
%o A074685 (define (gmA074685! s) (cond ((pair? s) (gmrobl! s) (gmA074685! (cdr s)))) s)



%I A074686
%S A074686 0,1,3,2,8,7,4,5,6,22,21,17,18,20,10,9,11,12,13,14,15,16,19,64,63,58,59,62,46,45,48,49,50,54,
%T A074686 55,57,61,27,26,23,24,25,29,28,30,31,32,33,34,35,36,38,37,39,40,41,42,43,44,47,51,52,53,56,
%U A074686 60,196,195,189,190,194,171,170,174,175,176,184,185,188,193,134,133,129,130,132,139,138,141
%N A074686 Permutation of natural numbers induced by the gatomorphism gmA074686! acting on the parenthesizations encoded by A014486/A063171.
%R A074686
%H A074686 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(With the complete Scheme source)</I>
%H A074686 <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>
%O A074686 0,3
%K A074686 nonn
%A A074686 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%D A074686
%Y A074686 Inverse of A074685. a(n) = A057163(A074690(A057163(n))). Occurs first time in A073200 as the row ???.
%o A074686 (Scheme function implementing this automorphism on list-structures:)
%o A074686 (define (gmA074686! s) (cond ((pair? s) (gmA074686! (cdr s)) (gmrobr! s))) s)






%I A074687
%S A074687 0,1,3,2,6,7,8,4,5,15,14,16,17,18,19,20,22,13,9,21,10,11,12,39,40,41,37,38,43,42,44,45,46,47,
%T A074687 48,49,50,52,51,53,54,55,60,61,62,34,33,63,36,27,23,56,57,64,35,24,58,26,32,29,59,25,28,30,
%U A074687 31,113,112,114,115,116,117,118,120,111,107,119,108,109,110,123,124,125,121,122,127,126,128
%N A074687 Permutation of natural numbers induced by the gatomorphism gmA074687! acting on the parenthesizations encoded by A014486/A063171.
%R A074687
%H A074687 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(With the complete Scheme source)</I>
%H A074687 <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>
%O A074687 0,3
%K A074687 nonn
%A A074687 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%D A074687
%Y A074687 Inverse of A074688 and also a(n) = A057163(A074688(A057163(n))). Cf. A074681-A074690. Occurs first time in A073200 as the row ???.
%o A074687 (Scheme function implementing this automorphism on list-structures:)
%o A074687 (define (gmA074687! s) (cond ((pair? s) (gmA074687! (car s)) (gmrobl! s) (gmA074687! (cdr s)))) s)



%I A074688
%S A074688 0,1,3,2,7,8,4,5,6,18,20,21,22,17,10,9,11,12,13,14,15,19,16,50,55,61,57,49,62,59,63,64,58,46,
%T A074688 45,54,48,26,27,23,24,25,29,28,30,31,32,33,34,35,36,38,37,39,40,41,51,52,56,60,42,43,44,47,
%U A074688 53,148,162,167,181,147,169,192,173,183,187,143,142,161,146,188,175,176,185,193,190,194,195
%N A074688 Permutation of natural numbers induced by the gatomorphism gmA074688! acting on the parenthesizations encoded by A014486/A063171.
%R A074688
%H A074688 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(With the complete Scheme source)</I>
%H A074688 <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>
%O A074688 0,3
%K A074688 nonn
%A A074688 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%D A074688
%Y A074688 Inverse of A074687 and also a(n) = A057163(A074687(A057163(n))). Cf. A074681-A074690. Occurs first time in A073200 as the row ???.
%o A074688 (Scheme function implementing this automorphism on list-structures:)
%o A074688 (define (gmA074688! s) (cond ((pair? s) (gmA074688! (cdr s)) (gmrobr! s) (gmA074688! (car s)))) s)



%I A074689
%S A074689 0,1,3,2,8,7,4,5,6,22,21,17,18,20,9,10,11,12,13,14,15,19,16,64,63,58,59,62,45,46,48,49,50,54,
%T A074689 55,61,57,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,51,52,60,56,42,43,44,47,
%U A074689 53,196,195,189,190,194,170,171,174,175,176,184,185,193,188,129,130,132,133,134,138,139,141
%N A074689 Permutation of natural numbers induced by the gatomorphism gmA074689! acting on the parenthesizations encoded by A014486/A063171.
%R A074689
%H A074689 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(With the complete Scheme source)</I>
%H A074689 <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>
%O A074689 0,3
%K A074689 nonn
%A A074689 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%D A074689
%Y A074689 Inverse of A074690. a(n) = A057163(A074685(A057163(n))). Cf. A074681-A074688. Occurs first time in A073200 as the row ???.
%o A074689 (Scheme function implementing this automorphism on list-structures:)
%o A074689 (define (gmA074689! s) (cond ((pair? s) (gmrobr! s) (gmA074689! (car s)))) s)




%I A074690
%S A074690 0,1,3,2,6,7,8,5,4,14,15,16,17,18,19,20,22,11,12,21,13,10,9,37,38,39,40,41,42,43,44,45,46,47,
%T A074690 48,49,50,51,52,53,54,55,60,61,62,28,29,63,30,31,32,56,57,64,33,34,59,36,25,26,58,35,27,24,
%U A074690 23,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128
%N A074690 Permutation of natural numbers induced by the gatomorphism gmA074690! acting on the parenthesizations encoded by A014486/A063171.
%R A074690
%H A074690 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> <I>(With the complete Scheme source)</I>
%H A074690 <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>
%O A074690 0,3
%K A074690 nonn
%A A074690 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%D A074690
%Y A074690 Inverse of A074689. a(n) = A057163(A074686(A057163(n))). Cf. A074681-A074688. Occurs first time in A073200 as the row ???.
%o A074690 (Scheme function implementing this automorphism on list-structures:)
%o A074690 (define (gmA074690! s) (cond ((pair? s) (gmA074690! (car s)) (gmrobl! s))) s)