A068497 Primes p such that 2*p+1 and 2*p-1 are composites.

13, 17, 43, 47, 59, 61, 67, 71, 73, 101, 103, 107, 109, 127, 137, 149, 151, 163, 167, 181, 193, 197, 223, 227, 241, 257, 263, 269, 277, 283, 311, 313, 317, 347, 349, 353, 373, 383, 389, 397, 401, 409, 421, 433, 449, 457, 461, 463, 467, 479, 487, 503, 521

Offset: 1

Author

Benoit Cloitre, Mar 25 2002

Keywords

• easy
• nonn

Comments

Subsequence of A053176. - Michel Marcus, Jan 12 2015

The sequence is infinite. Among others it contains all the primes of the form 15m+/-2. - Emmanuel Vantieghem, Sep 19 2016

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Programs

GAP

Filtered([1..530],p->IsPrime(p) and not IsPrime(2*p+1) and not IsPrime(2*p-1)); # Muniru A Asiru, Oct 16 2018

Magma

[p: p in PrimesUpTo(600) | not IsPrime(2*p+1) and not IsPrime(2*p-1)]; // Vincenzo Librandi, Jan 20 2015

Maple

select(p->isprime(p) and not isprime(2*p+1) and not isprime(2*p-1),[$1..530]); # Muniru A Asiru, Oct 16 2018

Mathematica

lst={};Do[p=Prime[n];If[ !PrimeQ[2*p-1]&&!PrimeQ[2*p+1],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, May 12 2010 *)
Select[Prime[Range[500]], ! PrimeQ[2*# - 1] && ! PrimeQ[2*# + 1] &] (* G. C. Greubel, Oct 15 2018 *)

PARI

listp(nn) = {forprime(p=2, nn, if (!isprime(2*p-1) && !isprime(2*p+1), print1(p, ", ")););} \\ Michel Marcus, Jan 12 2015