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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 (list; graph; refs; listen; history; text; internal format)
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.

Sequence in context: A093814 A212155 A269328 * A296493 A196821 A147710

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

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Last modified April 20 03:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)