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A059500 Primes p such that both q=(p-1)/2 and 2p+1=4q+3 are composite numbers. Intersection of A059456 and A053176. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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]

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..1000

C. K. Caldwell, Cunningham Chains

FORMULA

a(n) ~ n log n. - Charles R Greathouse IV, Jan 16 2013

EXAMPLE

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).

MATHEMATICA

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 *)

PROG

(PARI) is(n)=isprime(n)&&!isprime(n\2)&&!isprime(2*n+1) \\ Charles R Greathouse IV, Jan 16 2013

CROSSREFS

Cf. A005384, A005385, A053176, A059452-A059456, A007700, A005602, A023272, A023302, A023330, A156658.

Sequence in context: A098095 A249953 A180530 * A104213 A178550 A105896

Adjacent sequences:  A059497 A059498 A059499 * A059501 A059502 A059503

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 05 2001

STATUS

approved

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Last modified January 17 18:28 EST 2018. Contains 297829 sequences.