A309718 Numbers k such that the sums of the first k and k+2 primes are also prime.

2, 4, 12, 100, 122, 130, 204, 206, 214, 326, 328, 330, 332, 356, 458, 1024, 1148, 1190, 1418, 1474, 1476, 1500, 1524, 1630, 1842, 1948, 2128, 2130, 2184, 2436, 2448, 2536, 2686, 2688, 2784, 2796, 2898, 2980, 3112, 3562, 3682, 3806, 3936, 3944, 4114, 4318, 4332, 4364, 4376, 4412

Offset

1,1

Comments

The first run of four consecutive terms that differ by two, starts at k = 326.

The first run of five consecutive terms that differ by two, starts at k = 1195374. - Daniel Suteu, Aug 17 2019

Links

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

Example

For k=2, the sum of the first two primes 2+3 = 5 is prime. Additionally, the sum of the first k + 2=4 primes 2+3+5+7 = 17 is prime. So 2 is a term.
For k=6, the sum of the first six primes 2+3+5+7+11+13 = 41 is prime. But, the sum of the first k+2=8 primes 2+3+5+7+11+13+17+19 = 77 is not a prime. So 6 is not a term.

Maple

P:= [seq(ithprime(i), i=1..10002)]:
S:= ListTools:-PartialSums(P):
select(k -> isprime(S[k]) and isprime(S[k+2]), 2*[$1..5000]); # Robert Israel, Sep 01 2019

Prog

(PARI) isspp(n) = isprime(sum(i=1, n, prime(i))); \\ A013916
isok(n) = isspp(n) && isspp(n+2); \\ Michel Marcus, Aug 14 2019

Crossrefs

Cf. A013916.

Sequence in context: A259048 A228809 A326945 * A230814 A325502 A038791

Adjacent sequences: A309715 A309716 A309717 * A309719 A309720 A309721

Keyword

nonn

Author

Philip Mizzi, Aug 13 2019

Extensions

More terms from Michel Marcus, Aug 14 2019

Status

approved