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%I #39 Sep 08 2022 08:45:00
%S 7,13,17,19,31,37,43,47,59,61,67,71,73,79,97,101,103,107,109,127,137,
%T 139,149,151,157,163,167,181,193,197,199,211,223,227,229,241,257,263,
%U 269,271,277,283,307,311,313,317,331,337,347,349,353,367,373,379,383
%N Primes p such that 2p+1 is composite.
%C Primes not in A005384 = non-Sophie Germain primes.
%C Also, numbers n such that odd part of A005277(n) is prime. Proof by John Renze, Sep 30 2004
%C Sequence gives primes p such that B(2p) has denominator 6, where B(2n) are the Bernoulli numbers. - _Benoit Cloitre_, Feb 06 2002
%C Sequence gives all n such that the equation phi(x)=2n has no solution. - _Benoit Cloitre_, Apr 07 2002
%C A010051(a(n))*(1-A156660(a(n))) = 1; subsequence of A138887. - _Reinhard Zumkeller_, Feb 18 2009
%C Mersenne prime exponents > 3 must be in the union of this sequence and (A002144). - _Roderick MacPhee_, Jan 12 2017
%H T. D. Noe, <a href="/A053176/b053176.txt">Table of n, a(n) for n = 1..10000</a>
%H Lambert A'Campo, <a href="https://arxiv.org/abs/2006.06737">Every 7-Dimensional Abelian Variety over the p-adic Numbers has a Reducible L-adic Galois Representation</a>, arXiv:2006.06737 [math.NT], 2020.
%F a(n) ~ n log n. - _Charles R Greathouse IV_, Feb 20 2012
%e 17 is a term because 2*17 + 1 = 35 is composite.
%t Select[Prime[Range[1000]], ! PrimeQ[2 # + 1] &] (* _Vincenzo Librandi_, Jun 18 2015 *)
%o (PARI) list(lim)=select(p->!isprime(2*p+1),primes(primepi(lim))) \\ _Charles R Greathouse IV_, Jul 25 2011
%o (Magma) [p: p in PrimesUpTo(12200) | not IsPrime(2*p+1)]; // _Vincenzo Librandi_, Jun 18 2015
%Y Cf. A005384, A005385, A059452, A059453, A059454, A059455, A059456, A007700, A005602, A023272, A023302, A023330, A156543, A156542.
%K nonn,easy
%O 1,1
%A _Enoch Haga_, Feb 29 2000
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