A215540 Least k such that (2*n-1)*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m, or 0 if no such value exists.

1, 41, 7, 14, 67, 18759, 20, 229, 147, 6838, 41

Offset

1,2

Comments

(2*n-1)*2^a(n) + 1 is in A023394.

a(n) >= 7 for n > 1.

a(39279) = 0. No n < 39279 with a(n)=0 is known.

a(12)>2500000, a(13)>2500000, a(14)=455, a(15)=57 (see Ballinger and Keller link).

No, a(13)=2141884, found in 2011. - Jeppe Stig Nielsen, Sep 07 2019

Links

Table of n, a(n) for n=1..11.

Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300

Fermat factoring status, Prime factors of Fermat numbers

FermatSearch, Home page

PrimeGrid, Announcement of 25*2^2141884+1, related to a(13).

Eric Weisstein's World of Mathematics, Fermat Number

Mathematica

lst = {}; Do[k = 1; While[True, p = n*2^k + 1; If[PrimeQ[p] && IntegerQ@Log[2, MultiplicativeOrder[2, p]], AppendTo[lst, k]; Break[]]; k++], {n, 1, 9, 2}]; lst

Crossrefs

Cf. A000215, A033809.

Sequence in context: A106424 A126636 A095188 * A107813 A198162 A304581

Adjacent sequences: A215537 A215538 A215539 * A215541 A215542 A215543

Keyword

nonn,hard,more

Author

Arkadiusz Wesolowski, Aug 15 2012

Status

approved