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A304356 Primes that are the sum of three consecutive primes == 1 (mod 4). 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Apr 24 2019, from Maple *)

CROSSREFS

Cf. A002144, A304358.  Subset of A002145.

Sequence in context: A212266 A322919 A026050 * 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

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Last modified April 5 10:33 EDT 2020. Contains 333239 sequences. (Running on oeis4.)