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%I #20 Sep 08 2022 08:46:16
%S 37,163,15667,47287,120607,142543,234067,263047,263803,444607,607093,
%T 671353,1447153,1457857,1562983,2162323,2694157,2841337,2979043,
%U 3362143,3567337,4890307,5037433,5353987,5772097,6404773,6776023,7717873,9139453,9549373,10550467
%N Primes p such that p+2^4, p+2^6, p+2^8, p+2^10, p+2^12 and p+2^14 are all primes.
%H Dana Jacobsen, <a href="/A269859/b269859.txt">Table of n, a(n) for n = 1..10801</a>
%e The prime 37 is in the sequence, since 37 + 16 = 53, 37 + 64 = 101, 37 + 256 = 293, 37 + 1024 = 1061, 37 + 4096 = 4133 and 37 + 16384 = 16421 are all primes.
%e The prime 163 is in the sequence, since 163 + 16 = 179, 163 + 64 = 227, 163 + 256 = 419, 163 + 1024 = 1187, 163 + 4096 = 4259 and 163 + 16384 = 16547 are all primes.
%t m = Map[2^# &, 2 Range[2, 7]]; Select[Prime@ Range[10^6], Times @@ Boole@ PrimeQ[# + m] == 1 &] (* _Michael De Vlieger_, Jul 13 2016 *)
%o (Perl) use ntheory ":all"; say for sieve_prime_cluster(2,1e6, 16,64,256,1024,4096,16384); # _Dana Jacobsen_, Jul 13 2016
%o (Magma) [p: p in PrimesInInterval(2,12000000) | forall{i: i in [16,64,256,1024,4096,16384] | IsPrime(p+i)}]; // _Vincenzo Librandi_, Jul 16 2016
%Y Subsequence of A269259.
%Y Cf. A269257, A269258.
%K nonn
%O 1,1
%A _Debapriyay Mukhopadhyay_, Jul 12 2016
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