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A269259 Primes p such that p+2^4, p+2^6, p+2^8, p+2^10 and p+2^12 are all primes. 6
37, 163, 15667, 22093, 40177, 47287, 53593, 114577, 120607, 142543, 234067, 242377, 255907, 263047, 263803, 305407, 388117, 444607, 460387, 503287, 527143, 607093, 671353, 784897, 904663, 938947, 1063903, 1086493, 1172803, 1216807, 1233523, 1288543 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Dana Jacobsen, Table of n, a(n) for n = 1..10476

EXAMPLE

The prime 37 is in the sequence, since 37 + 16 = 53, 37 + 64 = 101, 37 + 256 = 293, 37 + 1024 = 1061 and 37 + 4096 = 4133 are all primes.

The prime 163 is in the sequence, since 163 + 16 = 179, 163 + 64 = 227, 163 + 256 = 419, 163 + 1024 = 1187 and 163 + 4096 = 4259 are all primes.

MATHEMATICA

m = {2^4, 2^6, 2^8, 2^10, 2^12}; Select[Prime@ Range[2*10^5], Times @@ Boole@ PrimeQ[# + m] == 1 &] (* Michael De Vlieger, Jul 13 2016 *)

PROG

(PARI) is(n) = for(k=2, 6, if(!ispseudoprime(2^(2*k)+n), return(0))); return(1)

forprime(p=1, 16e5, if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Jul 12 2016

(Perl) use ntheory ":all"; say for sieve_prime_cluster(2, 1e6, 16, 64, 256, 1024, 4096); # Dana Jacobsen, Jul 13 2016

(MAGMA) [p: p in PrimesInInterval(2, 1600000) | forall{i: i in [16, 64, 256, 1024, 4096] | IsPrime(p+i)}]; // Vincenzo Librandi, Jul 16 2016

CROSSREFS

Subsequence of A269258.

Cf. A269257.

Sequence in context: A250842 A083389 A142909 * A269859 A049496 A049497

Adjacent sequences:  A269256 A269257 A269258 * A269260 A269261 A269262

KEYWORD

nonn

AUTHOR

Debapriyay Mukhopadhyay, Jul 12 2016

STATUS

approved

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Last modified October 21 14:40 EDT 2019. Contains 328301 sequences. (Running on oeis4.)