A201364 Numbers k such that A057775(k) is the factor of a Fermat number 2^(2^m) + 1 for some m.

1, 2, 4, 7, 8, 14, 16, 25, 39, 41, 57, 67, 75, 120, 127, 147, 209, 229, 231, 290, 302, 320, 455, 547, 558, 747, 1553, 1947, 2027, 2458, 3313, 3508, 4262, 4727, 6210, 6393, 6539, 6838, 7312, 8242, 8557, 9431, 9450, 12189, 13252, 14254, 14280, 15164, 17909, 18759

Offset

1,2

Comments

Indices of Fermat factors in A057775.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..57

Wilfrid Keller, Fermat factoring status

Eric Weisstein's World of Mathematics, Fermat Number

Mathematica

lst = {}; Do[k = 1; While[! PrimeQ[p = (2*k - 1)*2^n + 1], k++]; If[IntegerQ[Log[2, MultiplicativeOrder[2, p]]], AppendTo[lst, n]], {n, 320}]; lst

Prog

(PARI) isok(n)=my(k=-1, p(k)=k*2^n+1, z(k)=znorder(Mod(2, p(k)))); until(isprime(p(k)), k=k+2); z(k)>>valuation(z(k), 2)==1; \\ Arkadiusz Wesolowski, May 26 2023

Crossrefs

Cf. A000215, A057775, A057778.

Sequence in context: A062846 A102824 A324588 * A225318 A308267 A177805

Adjacent sequences: A201361 A201362 A201363 * A201365 A201366 A201367

Keyword

nonn

Author

Arkadiusz Wesolowski, Nov 30 2011

Extensions

a(44)-a(50) from Arkadiusz Wesolowski, May 26 2023

Status

approved