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

%I

%S 7,37,163,337,757,967,1033,1303,2293,2377,2647,2713,3607,5023,6763,

%T 7417,8677,8803,9157,9277,10273,14683,14827,15313,15667,16417,20113,

%U 21163,21757,22093,24907,27043,27763,29803,29863,32173,34897,36793,36997,37783,38287,38977,39607

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

%H Charles R Greathouse IV, <a href="/A269257/b269257.txt">Table of n, a(n) for n = 1..10000</a>

%H Debapriyay Mukhopadhyay, <a href="/A269257/a269257_1.c.txt">C program to generate the terms of the sequences A269257, A269258, A269259, A269859 and A270203 up to 10^8</a>

%e The prime 7 is in the sequence because 7+16 = 23, 7+64 = 71 and 7+256 = 263 are all primes.

%e The prime 37 is in the sequence because 37+16 = 53, 37+64 = 101 and 37+256 = 293 are all primes.

%t Select[Prime[Range[10000]], PrimeQ[# + 2^4] && PrimeQ[# + 2^6] && PrimeQ[# + 2^8]&] (* _Jean-Fran├žois Alcover_, Jul 12 2016 *)

%t 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 *)

%o (PARI) is(n)=n%6==1 && isprime(n+16) && isprime(n+64) && isprime(n+256) && isprime(n) \\ _Charles R Greathouse IV_, Jul 12 2016

%o (Perl) use ntheory ":all"; say for sieve_prime_cluster(2,1e6, 16,64,256); # _Dana Jacobsen_, Jul 13 2016

%Y Subsequence of A002476, A049488, and A049490.

%K nonn

%O 1,1

%A _Debapriyay Mukhopadhyay_, Jul 12 2016

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Last modified June 16 21:35 EDT 2021. Contains 345080 sequences. (Running on oeis4.)