

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
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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] (* JeanFrançois 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



