A067774 Primes p such that p+2 is not a prime.

2, 7, 13, 19, 23, 31, 37, 43, 47, 53, 61, 67, 73, 79, 83, 89, 97, 103, 109, 113, 127, 131, 139, 151, 157, 163, 167, 173, 181, 193, 199, 211, 223, 229, 233, 241, 251, 257, 263, 271, 277, 283, 293, 307, 313, 317, 331, 337, 349, 353, 359, 367, 373, 379, 383, 389

Offset: 1

Author

Benoit Cloitre, Feb 06 2002

Keywords

• nonn
• easy

Comments

Primes n such that n!*B(n+1) is an integer where B(k) are the Bernoulli numbers.

All primes except for the lower members of twin primes - i.e. remove 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, ... - Gerard Schildberger, Feb 13 2005

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A049591.

Complement of A001359 in A000040, A025584, A007510.

Programs

Magma

[p: p in PrimesUpTo(400) | NextPrime(p)-p ne 2]; // Bruno Berselli, Apr 09 2013

Mathematica

f[n_]:=PrimeQ[n+2]; lst={}; Do[p=Prime[n]; If[ !f[p], AppendTo[lst,p]], {n,5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 17 2009 *)

PARI

is(n)=isprime(n)&&!isprime(n+2) \\ Charles R Greathouse IV, Jul 01 2013

Formula

Except for a(1)=2, a(n+1)=A049591(n).

a(n) ~ n log n. - Charles R Greathouse IV, Jul 01 2013

Extensions

Better description from Vladeta Jovovic, Dec 14 2002