A270203 - OEIS

%I #22 Sep 08 2022 08:46:16

%S 163,15667,234067,607093,671353,1447153,1457857,2162323,5772097,

%T 7717873,9139453,9549373,11170933,12039883,13243063,16442407,16836163,

%U 17784253,18116473,19433863,21960577,28209703,29175283,32380177,33890803,34613287,34682113

%N Primes p such that p+2^4, p+2^6, p+2^8, p+2^10, p+2^12, p+2^14 and p + 2^16 are all primes.

%H Dana Jacobsen, <a href="/A270203/b270203.txt">Table of n, a(n) for n = 1..10957</a>

%e The prime 163 is in the sequence, since 163 + 16 = 179, 163 + 64 = 227, 163 + 256 = 419, 163 + 1024 = 1187, 163 + 4096 = 4259, 163 + 16384 = 16547 and 163 + 65536 = 65699 are all primes.

%t m = {2^4, 2^6, 2^8, 2^10, 2^12, 2^14, 2^16}; Select[Prime@ Range[3*10^6], Times @@ Boole@ PrimeQ[# + m] == 1 &] (* _Michael De Vlieger_, Jul 13 2016 *)

%t Select[Prime[Range[22*10^5]],AllTrue[#+2^Range[4,16,2],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Dec 12 2018 *)

%o (Perl) use ntheory ":all"; say for sieve_prime_cluster(2,1e8, 16,64,256,1024,4096,16384,65536); # _Dana Jacobsen_, Jul 13 2016

%o (Magma) [p: p in PrimesInInterval(2,40000000) | forall{i: i in [16,64,256,1024,4096,16384,65536] | IsPrime(p+i)}]; // _Vincenzo Librandi_, Jul 16 2016

%Y Subsequence of A269859.

%Y Cf. A269257, A269258, A269259.

%K nonn

%O 1,1

%A _Debapriyay Mukhopadhyay_, Jul 12 2016