

A063377


Sophie Germain degree of n: number of iterations of n under f(k) = 2k+1 before we reach a number that is not a prime.


6



0, 5, 2, 0, 4, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
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OFFSET

1,2


COMMENTS

a(n) >= 1 means that n is prime; a(n) >= 2 means that is a Sophie Germain prime. Is the Sophie Germain degree always finite? Is it unbounded?


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000


EXAMPLE

a(2)=5 because 2, 5, 11, 23, 47 are prime but 95 is not.


PROG

(PARI) a(n) = {if (! isprime(n), return (0)); d = 1; k = n; while(isprime(p = 2*k+1), k = p; d++; ); return (d); } \\ Michel Marcus, Jul 22 2013


CROSSREFS

Cf. A005384, A063378, A093008, A093007, A292936.
See also Cunningham chains, A005602, A005603.
Sequence in context: A093814 A212155 A269328 * A296493 A196821 A333419
Adjacent sequences: A063374 A063375 A063376 * A063378 A063379 A063380


KEYWORD

nonn


AUTHOR

Reiner Martin (reinermartin(AT)hotmail.com), Jul 14 2001


EXTENSIONS

Term a(1) = 0 prepended by Antti Karttunen, Oct 09 2018


STATUS

approved



