%I A095355
%S A095355 0,0,0,3,3,5,15,13,10,13,25,22,97,85,203,359,625,1067,1880,3166,6068
%N A095355 Ratio A095106(n)/A095093(n) rounded down.
%F A095355 a(n) = 0 if A095093(n) is 0, otherwise a(n) = floor(A095106(n)/A095093(n).
%C A095355 This is the average diving index for those 4k+3 primes in range ]2^n,2^(n+1)] that "dive". See A095103.
%C A095355 The ratios before rounding are: 0, 0, 0, 3, 3, 5.666667, 15.666667, 13.166667, 10.142857, 13.926829, 25.805195, 22.118881, 97.536585, 85.237736, 203.39802, 359.470768, 625.039342, 1067.145123, 1880.907721, 3166.124599, 6068.683879.
%C A095355 Ratio (A095106(n)/A095093(n))/(A095109(n)/A095091(n)) goes as: 0, 0, 0, 1, 0.5, 0.428571, 0.4, 0.387097, 0.308824, 0.277027, 0.248387, 0.215361, 0.213383, 0.191474, 0.178036, 0.169496, 0.156814, 0.148329, 0.141456, 0.134383.
%Y A095355 A095356 gives the same ratios rounded to nearest integer. A095359 gives similar ratios computed for all 4k+3 integers.
%K A095355 nonn
%O A095355 1,4
%A A095355 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jun 12 2004



%I A095356
%S A095356 0,0,0,3,3,6,16,13,10,14,26,22,98,85,203,359,625,1067,1881,3166,6069
%N A095356 Ratio A095106(n)/A095093(n) rounded to nearest integer.
%F A095356 a(n) = 0 if A095093(n) is 0, otherwise a(n) = round(A095106(n)/A095093(n).
%Y A095356 A095355, where the same ratios are given round down.
%K A095356 nonn
%O A095356 1,4
%A A095356 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jun 12 2004

%I A095357
%S A095357 2,6,10,18,35,49,108,181,346,651,1236,2348,4240,8454,16537,30963,
%T A095357 60986,118814,225337,438305,854049
%N A095357 Ratio A095107(n)/A095008(n) rounded down.
%F A095357 a(n) = floor(A095107(n)/A095008(n).
%C A095357 This is the average length of maximum Dyck path prefix (i.e. non-diving portion) found in the "Legendre-vectors" of all 4k+3 primes in range ]2^n,2^(n+1)]. See A095104-A095105.
%C A095357 The ratios before rounding are: 2, 6, 10, 18, 35.333333, 49.428571, 108.461538, 181.545455, 346.702703, 651.295775, 1236.34375, 2348.779221, 4240.445455, 8454.26518, 16537.703752, 30963.160864, 60986.990505, 118814.20247, 225337.874981, 438305.90522, 854049.74263.
%C A095357 Ratio (A095107(n)/A095008(n))/(A095110(n)/A000079(n-2)) goes as: 1, 1, 0.5, 0.75, 0.375, 0.4375, 0.40625, 0.34375, 0.289062, 0.277344, 0.25, 0.225586, 0.214844, 0.197021, 0.185425, 0.175293, 0.16391, 0.155701, 0.14756, 0.140224.
%Y A095357 A095358 gives the same ratios rounded to nearest integer. A095361 gives similar ratios computed for all 4k+3 integers.
%K A095357 nonn
%O A095357 1,1
%A A095357 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jun 12 2004

%I A095358
%S A095358 2,6,10,18,35,49,108,182,347,651,1236,2349,4240,8454,16538,30963,
%T A095358 60987,118814,225338,438306,854050
%N A095358 Ratio A095107(n)/A095008(n) rounded to nearest integer.
%F A095358 a(n) = round(A095107(n)/A095008(n).
%Y A095358 A095357, where the same ratios are given round down.
%K A095358 nonn
%O A095358 1,1
%A A095358 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jun 12 2004

%I A095359
%S A095359 0,0,0,3,6,5,12,12,20,24,42,58,97,140,286,478,841,1504,2788,5048
%N A095359 Ratio A095109(n)/A095091(n) rounded down.
%F A095359 a(n) = 0 if A095091(n) is 0, otherwise a(n) = floor(A095109(n)/A095091(n).
%C A095359 This is the average diving index for those 4k+3 integers in range ]2^n,2^(n+1)] that "dive". See A095101.
%C A095359 The ratios before rounding are: 0, 0, 0, 3, 6.5, 5.714286, 12.933333, 12.548387, 20.691176, 24.635135, 42.903226, 58.98494, 97.742751, 140.742413, 286.896704, 478.786471, 841.487894, 1504.108692, 2788.84881, 5048.608416.
%Y A095359 A095360 gives the same ratios rounded to nearest integer. A095355 gives similar ratios computed only for 4k+3 primes.
%K A095359 nonn
%O A095359 1,4
%A A095359 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jun 12 2004

%I A095360
%S A095360 0,0,0,3,7,6,13,13,21,25,43,59,98,141,287,479,841,1504,2789,5049
%N A095360 Ratio A095109(n)/A095091(n) rounded to nearest integer.
%F A095360 a(n) = 0 if A095091(n) is 0, otherwise a(n) = round(A095109(n)/A095091(n).
%Y A095360 Comments at A095359, where the same ratios are given rounded down.
%K A095360 nonn
%O A095360 1,4
%A A095360 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jun 12 2004

%I A095361
%S A095361 2,6,12,20,37,52,106,200,369,657,1226,2191,4268,8076,15291,28931,
%T A095361 55124,105982,202482,391505
%N A095361 Ratio A095110(n)/A000079(n-2) rounded down.
%F A095361 a(1) = 2, a(n) = floor(A095110(n)/A000079(n-2)) for n > 1.
%C A095361 This is the average length of maximum Motzkin path prefix (i.e. non-diving portion) found in the "Jacobi-vectors" of all 4k+3 integers in range ]2^n,2^(n+1)]. See A095269-A095270.
%C A095361 The ratios before rounding are: 2, 6, 12, 20, 37.875, 52.9375, 106.28125, 200.25, 369.179687, 657.445312, 1226.675781, 2191.126953, 4268.283691, 8076.054443, 15291.317139, 28931.598755, 55124.513184, 105982.564758, 202482.488968, 391505.689705.
%Y A095361 A095362 gives the same ratios rounded to nearest integer. A095357 gives similar ratios computed only for 4k+3 primes.
%K A095361 nonn
%O A095361 1,1
%A A095361 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jun 12 2004

%I A095362
%S A095362 2,6,12,20,38,53,106,200,369,657,1227,2191,4268,8076,15291,28932,
%T A095362 55125,105983,202482,391506
%N A095362 Ratio A095110(n)/A000079(n-2) rounded to nearest integer.
%F A095362 a(1) = 2, a(n) = round(A095110(n)/A000079(n-2)) for n > 1.
%Y A095362 Comments at A095361, where the same ratios are given rounded down.
%K A095362 nonn
%O A095362 1,1
%A A095362 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jun 12 2004