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

Author

Arkadiusz Wesolowski, Nov 30 2011

Keywords

• nonn

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

Crossrefs

Cf. A000215, A057775, A057778.

Programs

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

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

Extensions

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