A331135 a(n) = Sum_{primes p <= n} r_2(p-1)/4, where r_2(n) = A004018(n).

0, 1, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 17

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Yoichi Motohashi, On the distribution of prime numbers which are of the form x^2+y^2+1, Acta Arith. 16 (1969/70), 351-363. MR0288086 (44 #5284).

Mathematica

Accumulate[Table[If[PrimeQ[n], SquaresR[2, n-1], 0], {n, 1, 100}]/4] (* Amiram Eldar, Apr 23 2024 *)

Crossrefs

Cf. A004018, A331134.

Sequence in context: A368991 A147954 A105047 * A089881 A251547 A084320

Adjacent sequences: A331132 A331133 A331134 * A331136 A331137 A331138

Keyword

nonn,changed

Author

N. J. A. Sloane, Jan 11 2020

Status

approved