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

1,1

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Subsequence of A002476, A049488, and A049490.

Sequence in context: A036678 A085720 A201962 * A269258 A247308 A175284

Adjacent sequences: A269254 A269255 A269256 * A269258 A269259 A269260

Keyword

nonn

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Status

approved