A269257 Primes p such that p+2^4, p+2^6 and p+2^8 are all primes.

7, 37, 163, 337, 757, 967, 1033, 1303, 2293, 2377, 2647, 2713, 3607, 5023, 6763, 7417, 8677, 8803, 9157, 9277, 10273, 14683, 14827, 15313, 15667, 16417, 20113, 21163, 21757, 22093, 24907, 27043, 27763, 29803, 29863, 32173, 34897, 36793, 36997, 37783, 38287, 38977, 39607

Offset: 1

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Keywords

• nonn

Examples

			The prime 7 is in the sequence because 7+16 = 23, 7+64 = 71 and 7+256 = 263 are all primes.
The prime 37 is in the sequence because 37+16 = 53, 37+64 = 101 and 37+256 = 293 are all primes.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Debapriyay Mukhopadhyay, C program to generate the terms of the sequences A269257, A269258, A269259, A269859 and A270203 up to 10^8

Crossrefs

Subsequence of A002476, A049488, and A049490.

Programs

Mathematica

Select[Prime[Range[10000]], PrimeQ[# + 2^4] && PrimeQ[# + 2^6] && PrimeQ[# + 2^8]&] (* Jean-François Alcover, Jul 12 2016 *)
With[{c=2^Range[4,8,2]},Select[Prime[Range[4200]],AllTrue[#+c,PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 21 2017 *)

PARI

is(n)=n%6==1 && isprime(n+16) && isprime(n+64) && isprime(n+256) && isprime(n) \\ Charles R Greathouse IV, Jul 12 2016

Perl

use ntheory ":all"; say for sieve_prime_cluster(2,1e6, 16,64,256); # Dana Jacobsen, Jul 13 2016

Formula

A049488 INTERSECT A049490 INTERSECT A361483. - R. J. Mathar, Mar 26 2024