1,1

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.

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

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

Sequence in context: A140777 A050844 A077626 this_sequence A095358 A084481 A006553

Adjacent sequences: A095354 A095355 A095356 this_sequence A095358 A095359 A095360

nonn

Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jun 12 2004