A304356 Primes that are the sum of three consecutive primes == 1 (mod 4).

59, 83, 107, 131, 223, 307, 359, 443, 479, 547, 571, 619, 659, 827, 887, 967, 1039, 1187, 1231, 1303, 1367, 1427, 1571, 1619, 1667, 1831, 1871, 1987, 2011, 2087, 2143, 2251, 2287, 2339, 2459, 2503, 2539, 2687, 2927, 3019, 3067, 3259, 3299, 3323, 3463, 3527, 3607, 3631, 3659, 3863, 3919, 4219

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The first three primes == 1 (mod 4) are 5, 13, 17, but 5+13+17=35 is not prime.
The second, third and fourth primes == 1 (mod 4) are 13, 17, 29, and 13+17+29=59 is prime, so a(1) = 59.

Maple

N:= 2000: # to use primes <= N that == 1 (mod 4)
P:= select(isprime, [seq(i, i=1..N, 4)]):
select(isprime, P[1..-3]+P[2..-2]+P[3..-1]);

Mathematica

M = 2000;
P = Select[Range[1, M, 4], PrimeQ];
Select[P[[1;; -3]] + P[[2;; -2]] + P[[3;; -1]], PrimeQ] (* Jean-François Alcover, Apr 24 2019, from Maple *)
Select[Total/@Partition[Select[Prime[Range[250]], Mod[#, 4]==1&], 3, 1], PrimeQ] (* Harvey P. Dale, Aug 20 2022 *)

Crossrefs

Cf. A002144, A304358. Subset of A002145.

Sequence in context: A322919 A026050 A347804 * A283146 A068209 A139958

Adjacent sequences: A304353 A304354 A304355 * A304357 A304358 A304359

Keyword

nonn

Author

J. M. Bergot and Robert Israel, May 11 2018

Status

approved