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

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Last modified October 3 14:56 EDT 2022. Contains 357237 sequences. (Running on oeis4.)