%I #18 Apr 27 2019 03:38:18

%S 37,53,73,97,149,173,197,233,293,337,397,421,509,569,601,661,1129,

%T 1181,1289,1373,1409,1433,1493,1721,1949,2137,2281,2633,2677,2777,

%U 2833,3041,3089,3121,3581,3769,3821,3853,3877,3929,4013,4093,4289,4337,4357,4441,4597,4733,4909,4957,5381,5501,5657

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

%H Robert Israel, <a href="/A304358/b304358.txt">Table of n, a(n) for n = 1..10000</a>

%e The first three primes == 3 (mod 4) are 3, 7, 11, but 3+7+11=21 is not prime.

%e The second, third and fourth primes == 3 (mod 4) are 7, 11, 19, and 7+11+19=37 is prime, so a(1)=37.

%p N:= 2000: # to use primes <= N that == 1 (mod 4)

%p P:= select(isprime, [seq(i, i=1..N, 4)]):

%p select(isprime, P[1..-3]+P[2..-2]+P[3..-1]);

%t M = 2000;

%t P = Select[Range[3, M, 4], PrimeQ];

%t Select[P[[1;;-3]] + P[[2;;-2]] + P[[3;;-1]], PrimeQ] (* _Jean-François Alcover_, Apr 27 2019, from Maple *)

%Y Cf. A002145, A304356. Subset of A002144.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, May 11 2018