A179013 Greatest k <= n such that 2^n-2^k+1 is prime, or 0 if no such prime exists.

0, 1, 2, 2, 4, 2, 5, 6, 8, 8, 5, 2, 9, 12, 9, 12, 16, 0, 12, 18, 0, 2, 20, 18, 18, 16, 21, 16, 26, 18, 27, 30, 20, 22, 19, 20, 25, 36, 23, 32, 37, 38, 41, 38, 9, 38, 25, 44, 41, 44, 17, 48, 50, 38, 52, 32, 38, 34, 48, 18, 54

Offset

1,3

Comments

For the first 8300 terms, there are 291 values of n such that a(n)=0 and 6927 values of n with a(n) >= n/2.

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Mathematica

Table[k=n; While[k>0 && ! PrimeQ[2^n-2^k+1], k--]; k, {n, 100}]

Prog

(Sage)
A179013 = lambda n: next((k for k in reversed([1..floor(log(2**n+1, 2))]) if is_pseudoprime(2**n-2**k+1)), 0) # D. S. McNeil, Jan 12 2011
(PARI) a(n) = {my(k=n); while (!isprime(2^n-2^k+1), k--; if (k==0, return (0))); k; } \\ Michel Marcus, Sep 21 2019

Crossrefs

Cf. A106821, A178993.

Sequence in context: A133181 A286280 A290088 * A090397 A339176 A328729

Adjacent sequences: A179010 A179011 A179012 * A179014 A179015 A179016

Keyword

nonn

Author

Pierre CAMI, Jan 12 2011

Status

approved