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

1,1

Comments

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.

Links

Table of n, a(n) for n=1..21.

Formula

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

Crossrefs

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

Sequence in context: A328960 A282428 A174316 * A095358 A084481 A006553

Adjacent sequences: A095354 A095355 A095356 * A095358 A095359 A095360

Keyword

nonn

Author

Antti Karttunen, Jun 12 2004

Status

approved