A095107 -id:A095107 - cp's OEIS frontend

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

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)).

A095358 Ratio A095107(n)/A095008(n) rounded to nearest integer.

Original entry on oeis.org

2, 6, 10, 18, 35, 49, 108, 182, 347, 651, 1236, 2349, 4240, 8454, 16538, 30963, 60987, 118814, 225338, 438306, 854050

Offset: 1

Antti Karttunen, Jun 12 2004

Cf. A095357, where the same ratios are given round down.

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

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

Original entry on oeis.org

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