A049493 Numbers n such that n and n+4^k are all primes for k=1,2,3.

3, 7, 37, 43, 67, 163, 757, 823, 967, 1087, 1213, 1303, 1423, 2293, 2377, 3187, 3343, 3847, 5653, 5923, 8677, 8803, 9157, 9277, 9787, 11257, 11617, 11923, 12097, 13693, 14653, 14767, 14827, 15667, 15733, 16417, 18127, 18397, 20113, 20743, 26293

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			3, 3+4=7, 3+16=19, 3+64=67 are all primes.
		

Links

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

Crossrefs

Subsequence of A049492.

Programs

Mathematica

Select[Prime[Range[3000]],And@@PrimeQ[#+4^{1,2,3}]&] (* Harvey P. Dale, Dec 26 2013 *)
Select[Prime[Range[3000]],AllTrue[#+{4,16,64},PrimeQ]&] (* Harvey P. Dale, Dec 29 2024 *)

PARI

isok(n) = isprime(n) && isprime(n+4) && isprime(n+16) && isprime(n+64); \\ Michel Marcus, Dec 22 2013

Formula

A049492 INTERSECT A049490. - R. J. Mathar, Mar 26 2024