A118480 (n-th 4k+1 prime minus n-th 4k+3 prime minus two)/4.

0, 1, 1, 2, 3, 2, 2, 3, 3, 5, 6, 5, 6, 2, 7, 5, 6, 8, 7, 7, 7, 12, 10, 10, 11, 11, 12, 10, 10, 12, 11, 13, 10, 10, 10, 10, 9, 8, 7, 9, 3, 4, 4, 4, 11, 13, 15, 17, 19, 19, 22, 19, 16, 13, 17, 16, 15, 16, 14, 17, 16, 21, 24, 19, 19, 13, 17, 17, 19, 19, 16, 11, 13, 13, 22, 19, 19, 17, 22

Offset: 1

Author

Clark Kimberling and Robert G. Wilson v, May 04 2006

Keywords

• sign

Comments

Zero occurs infinitely often as do the negative numbers.

First occurrence of a(n) beginning with 0: 1, 2, 4, 5, 42, 10, 11, 15, 18, 37, 23, 25, 22, 32, 59, 47, 53, 48, 83, 49, 110, 62, 51, 82, 63, 170, ...,

The first negative term is at n=1473. - T. D. Noe, Apr 09 2009

Links

• T. D. Noe, Table of n, a(n) for n=1..2000

Crossrefs

Cf. A022757, A007350, A007351, A038691.

Programs

Mathematica

(Select[1 + 4Range@245, PrimeQ@# &] - Select[ -1 + 4Range@225, PrimeQ@# &] - 2)/4

Formula

a(n) = (A002144(n) - A002145(n) - 2)/4.