A304358 Primes that are the sum of three consecutive primes == 3 (mod 4).

37, 53, 73, 97, 149, 173, 197, 233, 293, 337, 397, 421, 509, 569, 601, 661, 1129, 1181, 1289, 1373, 1409, 1433, 1493, 1721, 1949, 2137, 2281, 2633, 2677, 2777, 2833, 3041, 3089, 3121, 3581, 3769, 3821, 3853, 3877, 3929, 4013, 4093, 4289, 4337, 4357, 4441, 4597, 4733, 4909, 4957, 5381, 5501, 5657

Offset

1,1

Links

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

Example

The first three primes == 3 (mod 4) are 3, 7, 11, but 3+7+11=21 is not prime.
The second, third and fourth primes == 3 (mod 4) are 7, 11, 19, and 7+11+19=37 is prime, so a(1)=37.

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[3, M, 4], PrimeQ];
Select[P[[1;; -3]] + P[[2;; -2]] + P[[3;; -1]], PrimeQ] (* Jean-François Alcover, Apr 27 2019, from Maple *)

Crossrefs

Cf. A002145, A304356. Subset of A002144.

Sequence in context: A101938 A060330 A302720 * A214755 A101940 A330339

Adjacent sequences: A304355 A304356 A304357 * A304359 A304360 A304361

Keyword

nonn

Author

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

Status

approved