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A059500
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Primes p such that both q=(p-1)/2 and 2p+1=4q+3 are composite numbers. Intersection of A059456 and A053176.
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7
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13, 17, 19, 31, 37, 43, 61, 67, 71, 73, 79, 97, 101, 103, 109, 127, 137, 139, 149, 151, 157, 163, 181, 193, 197, 199, 211, 223, 229, 241, 257, 269, 271, 277, 283, 307, 311, 313, 317, 331, 337, 349, 353, 367, 373, 379, 389, 397, 401, 409, 421, 433, 439, 449
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OFFSET
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1,1
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COMMENTS
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Primes which are neither safe nor of Sophie Germain type.
Primes not in Cunningham chains of the first kind. - Alonso del Arte, Jun 30 2005
A010051(a(n))*(1-A156660(a(n)))*(1-A156659(a(n))) = 1; A156878 gives numbers of these numbers <= n. [From Reinhard Zumkeller, Feb 18 2009]
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..1000
C. K. Caldwell, Cunningham Chains
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FORMULA
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a(n) ~ n log n. - Charles R Greathouse IV, Jan 16 2013
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EXAMPLE
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Prime p=17 is here because both 35 and 8 are composite numbers. Such primes fall "out of" any Cunningham chain of first kind (or generate Cunningham chains of 0-length).
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MATHEMATICA
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Complement[Prime[Range[100]], Select[Prime[Range[100]], PrimeQ[2# + 1] &], Select[Prime[Range[100]], PrimeQ[(# - 1)/2] &]] (Delarte)
Select[Prime[Range[100]], !PrimeQ[q=2#+1]&&!PrimeQ[(#-1)/2]&] (* Zak Seidov, Mar 09 2013 *)
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PROG
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(PARI) is(n)=isprime(n)&&!isprime(n\2)&&!isprime(2*n+1) \\ Charles R Greathouse IV, Jan 16 2013
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CROSSREFS
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Cf. A005384, A005385, A053176, A059452-A059456, A007700, A005602, A023272, A023302, A023330, A156658.
Sequence in context: A099184 A098095 A180530 * A104213 A178550 A105896
Adjacent sequences: A059497 A059498 A059499 * A059501 A059502 A059503
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Feb 05 2001
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STATUS
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approved
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