A304356 - OEIS

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

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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]);