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A053176
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Primes p such that 2p+1 is composite.
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27
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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
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OFFSET
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1,1
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COMMENTS
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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. [From Reinhard Zumkeller, Feb 18 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) ~ n log n. [Charles R Greathouse IV, Feb 20 2012]
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EXAMPLE
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17 is a term because 2*17+1=35 is composite.
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MATHEMATICA
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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
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PROG
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(PARI) list(lim)=select(p->!isprime(2*p+1), primes(primepi(lim))) \\ Charles R Greathouse IV, Jul 25 2011
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CROSSREFS
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Cf. A005384, A005385, A059452, A059453, A059454, A059455, A059456, A007700, A005602, A023272, A023302, A023330, A156543, A156542.
Sequence in context: A090863 A045979 A079699 * A032669 A147603 A106084
Adjacent sequences: A053173 A053174 A053175 * A053177 A053178 A053179
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KEYWORD
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easy,nonn,changed
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AUTHOR
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Enoch Haga, Feb 29 2000
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STATUS
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approved
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