A095104 -id:A095104 - cp's OEIS frontend

A095105 Length of maximal Dyck path prefix in the Legendre-vector of the n-th 4k+3 prime (A002145(n)).

2, 6, 10, 2, 22, 30, 2, 46, 58, 2, 70, 78, 82, 102, 6, 6, 130, 2, 150, 2, 166, 10, 190, 198, 2, 12, 60, 238, 250, 262, 270, 2, 2, 310, 2, 6, 358, 44, 2, 382, 418, 430, 438, 6, 6, 34, 478, 6, 34, 2, 502, 2, 2, 562, 2, 14, 598, 606, 2, 14, 2, 646, 658, 6, 2, 718

Offset: 1

Antti Karttunen, Jun 01 2004

nonn

A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

a(n)=A095104(n)-1 modulo A002145(n). Cf. A095107, A095270.

A095106 Sum of diving indices of all 4k+3 primes in range ]2^n,2^(n+1)].

Original entry on oeis.org

0, 0, 0, 3, 3, 17, 94, 158, 213, 571, 1987, 3163, 27993, 45176, 205432, 707079, 2319521, 7603409, 25967812, 83981455, 310267532

Offset: 1

Antti Karttunen, Jun 01 2004

nonn

A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Cf. A095104, A095107, A095109.

A095108 Diving index of the n-th diving 4k+3 prime (A095103(n)).

Original entry on oeis.org

3, 3, 3, 7, 7, 3, 3, 11, 3, 13, 61, 3, 3, 3, 7, 45, 3, 7, 7, 35, 7, 35, 3, 3, 3, 3, 15, 3, 15, 3, 7, 3, 45, 3, 3, 3, 7, 7, 3, 3, 3, 7, 7, 67, 3, 7, 3, 7, 3, 7, 57, 7, 3, 7, 15, 7, 45, 7, 23, 3, 3, 11, 7, 3, 89, 13, 55, 3, 45, 35, 3, 7, 7, 3, 3, 3, 13, 7, 15, 3, 19, 3, 7, 3, 7, 3, 99

Offset: 1

Antti Karttunen, Jun 01 2004

nonn

A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Nonzero terms of A095104. Cf. A095271.

A095357 Ratio A095107(n)/A095008(n) rounded down.

Original entry on oeis.org

2, 6, 10, 18, 35, 49, 108, 181, 346, 651, 1236, 2348, 4240, 8454, 16537, 30963, 60986, 118814, 225337, 438305, 854049

Offset: 1

Antti Karttunen, Jun 12 2004

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.
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.
Ratio (A095107(n)/A095008(n))/(A095110(n)/A000079(n-2)) starts as follows: 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.

A095358 gives the same ratios rounded to nearest integer. A095361 gives similar ratios computed for all 4k+3 integers.

a(n) = floor(A095107(n)/A095008(n)).

cp's OEIS Frontend

A095105 Length of maximal Dyck path prefix in the Legendre-vector of the n-th 4k+3 prime (A002145(n)).

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A095106 Sum of diving indices of all 4k+3 primes in range ]2^n,2^(n+1)].

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A095108 Diving index of the n-th diving 4k+3 prime (A095103(n)).

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A095357 Ratio A095107(n)/A095008(n) rounded down.

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