A095104 Diving index of the n-th 4k+3 prime (A002145(n)).

0, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 7, 7, 0, 3, 0, 3, 0, 11, 0, 0, 3, 13, 61, 0, 0, 0, 0, 3, 3, 0, 3, 7, 0, 45, 3, 0, 0, 0, 0, 7, 7, 35, 0, 7, 35, 3, 0, 3, 3, 0, 3, 15, 0, 0, 3, 15, 3, 0, 0, 7, 3, 0, 45, 3, 0, 0, 3, 3, 7, 7, 0, 3, 0, 3, 0, 3, 0, 0, 7, 7, 0, 0, 0, 67, 0, 0, 3, 0

Offset

1,4

Comments

Diving index of an odd number n is the first integer u > 1 where Sum_{i=1..u} J(i/n) results -1 and zero if never. Here J(i/n) is Jacobi symbol of i and n, which reduces to a Legendre symbol L(i/n) when n is a prime.

Links

Table of n, a(n) for n=1..92.

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

Crossrefs

a(n)=A095105(n)+1 modulo A002145(n). Cf. A095106, A095108 (same sequence with zeros removed), A095269.

Sequence in context: A362313 A350914 A346607 * A021337 A361824 A293903

Adjacent sequences: A095101 A095102 A095103 * A095105 A095106 A095107

Keyword

nonn

Author

Antti Karttunen, Jun 01 2004

Status

approved