A278138 Primes p such that p+2, 3*p+2 and 3*p+8 are also primes.

3, 5, 17, 197, 1427, 1667, 2087, 4157, 4217, 8387, 8597, 10037, 11117, 11717, 15287, 17417, 20147, 25847, 29207, 33347, 33827, 34847, 35897, 36527, 47657, 56237, 57527, 60257, 63197, 63587, 69497, 75167, 77477, 89657, 93887, 96797, 99347, 99527, 100547

Offset

1,1

Comments

If k = (a(n)+2)*(3*a(n)+2), then A000203(k) = A000203(k-A000005(k)), see Robert Israel's comment at A277273.

Links

Iain Fox, Table of n, a(n) for n = 1..10000 (first 4356 terms from Robert Israel)

Maple

select(p -> isprime(3*p+8) and isprime(3*p+2) and isprime(p+2) and isprime(p), [3, seq(i, i=5..10^6, 6)]); # Robert Israel, Nov 23 2016

Mathematica

Select[Prime[Range[10000]], Union[PrimeQ/@{# + 2, 3 # + 2, 3 # + 8}] == {True}&]

Prog

(MATLAB)
P = primes(10^6);
P1 = intersect(P, P-2);
P1 = intersect(P1, (P-2)/3);
P1 = intersect(P1, (P-8)/3) % Robert Israel, Nov 23 2016
(Magma) [p: p in PrimesUpTo(100000) | IsPrime(p+2) and IsPrime(3*p+2) and IsPrime(3*p+8)]; // Vincenzo Librandi, Nov 23 2016
(PARI) isok(p) = isprime(p) && isprime(p+2) && isprime(3*p+2) && isprime(3*p+8); \\ Michel Marcus, Dec 17 2017

Crossrefs

Cf. A000040, A277273.

Subsequence of A001359.

Sequence in context: A083213 A171271 A056826 * A273870 A272060 A333873

Adjacent sequences: A278135 A278136 A278137 * A278139 A278140 A278141

Keyword

nonn,easy

Author

Ivan N. Ianakiev, Nov 23 2016

Status

approved