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 A053176 Primes p such that 2p+1 is composite. 27

%I

%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. [From _Reinhard Zumkeller_, Feb 18 2009]

%H T. D. Noe, <a href="/A053176/b053176.txt">Table of n, a(n) for n = 1..10000</a>

%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 a={};Do[p=Prime[n];If[ !PrimeQ[2*p+1],AppendTo[a,p]],{n,8^2}];a A115058 Primes p that are also the largest prime factor of p(p^2-1)(3p+2)/24. - _Vladimir Joseph Stephan Orlovsky_, Apr 29 2008

%o (PARI) list(lim)=select(p->!isprime(2*p+1),primes(primepi(lim))) \\ _Charles R Greathouse IV_, Jul 25 2011

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

%K easy,nonn,changed

%O 1,1

%A _Enoch Haga_, Feb 29 2000

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