A053176 Primes p such that 2p+1 is composite.

7, 13, 17, 19, 31, 37, 43, 47, 59, 61, 67, 71, 73, 79, 97, 101, 103, 107, 109, 127, 137, 139, 149, 151, 157, 163, 167, 181, 193, 197, 199, 211, 223, 227, 229, 241, 257, 263, 269, 271, 277, 283, 307, 311, 313, 317, 331, 337, 347, 349, 353, 367, 373, 379, 383

Offset: 1

Author

Enoch Haga, Feb 29 2000

Keywords

• nonn
• easy

Comments

Primes not in A005384 = non-Sophie Germain primes.

Also, numbers n such that odd part of A005277(n) is prime. Proof by John Renze, Sep 30 2004

Sequence gives primes p such that B(2p) has denominator 6, where B(2n) are the Bernoulli numbers. - Benoit Cloitre, Feb 06 2002

Sequence gives all n such that the equation phi(x)=2n has no solution. - Benoit Cloitre, Apr 07 2002

A010051(a(n))*(1-A156660(a(n))) = 1; subsequence of A138887. - Reinhard Zumkeller, Feb 18 2009

Mersenne prime exponents > 3 must be in the union of this sequence and (A002144). - Roderick MacPhee, Jan 12 2017

Examples

			17 is a term because 2*17 + 1 = 35 is composite.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Lambert A'Campo, Every 7-Dimensional Abelian Variety over the p-adic Numbers has a Reducible L-adic Galois Representation, arXiv:2006.06737 [math.NT], 2020.

Crossrefs

Cf. A005384, A005385, A059452, A059453, A059454, A059455, A059456, A007700, A005602, A023272, A023302, A023330, A156543, A156542.

Programs

Magma

[p: p in PrimesUpTo(12200) | not IsPrime(2*p+1)]; // Vincenzo Librandi, Jun 18 2015

Mathematica

Select[Prime[Range[1000]], ! PrimeQ[2 # + 1] &] (* Vincenzo Librandi, Jun 18 2015 *)

PARI

list(lim)=select(p->!isprime(2*p+1),primes(primepi(lim))) \\ Charles R Greathouse IV, Jul 25 2011

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Feb 20 2012