A049493 -id:A049493 - cp's OEIS frontend

A049492 Primes p such that p+4 and p+16 are also primes.

3, 7, 13, 37, 43, 67, 97, 163, 223, 277, 463, 487, 643, 757, 823, 937, 967, 1087, 1093, 1213, 1303, 1423, 1483, 1567, 1597, 1693, 1873, 2083, 2137, 2293, 2377, 2617, 2683, 2953, 3187, 3343, 3847, 3907, 4003, 4447, 4783, 5503, 5653, 5923, 6547, 6967, 6997

Offset: 1

Labos Elemer

nonn

All terms > 3 are == 1 (mod 6). - Zak Seidov, Sep 05 2014

Intersection of A023200 and A049488. - Michel Marcus, Sep 05 2014

			3, 3+4 = 7, 3+16 = 19 are all primes.

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A023200, A049488, A049493.

Select[Prime[Range[900]],And@@PrimeQ[#+{4,16}]&] (* Harvey P. Dale, Jan 17 2011 *)

lista(nn) = forprime (n=1, nn, if (isprime(n+4) && isprime(n+16), print1(n, ", "))); \\ Michel Marcus, Sep 05 2014

A049494 a(n) and a(n)+4^k are primes at least for k=1,2,3,4.

Original entry on oeis.org

7, 37, 163, 757, 967, 1303, 2293, 2377, 8677, 8803, 9157, 9277, 14827, 15667, 16417, 20113, 27763, 29863, 41953, 53593, 56527, 56893, 61027, 67153, 69763, 74827, 79333, 83203, 90007, 95467, 111577, 129277, 135193, 137383, 142543, 151783

Offset: 1

Labos Elemer

nonn

			7,7+4=11,7+16=23,7+64=71,7+256=263 are all primes: it is the smallest such quintet.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A023200, A049492, A049493, A049495-A049500.

Select[Prime[Range[15000]],AllTrue[#+{4,16,64,256},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 22 2018 *)

isok(n) = isprime(n) && isprime(n+4) && isprime(n+4^2) && isprime(n+4^3) && isprime(n+4^4); \\ Michel Marcus, Dec 31 2013

cp's OEIS Frontend

A049492 Primes p such that p+4 and p+16 are also primes.

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