A201364 - OEIS

A201364

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

%I #28 May 30 2023 07:46:05

%S 1,2,4,7,8,14,16,25,39,41,57,67,75,120,127,147,209,229,231,290,302,

%T 320,455,547,558,747,1553,1947,2027,2458,3313,3508,4262,4727,6210,

%U 6393,6539,6838,7312,8242,8557,9431,9450,12189,13252,14254,14280,15164,17909,18759

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

%C Indices of Fermat factors in A057775.

%H Arkadiusz Wesolowski, <a href="/A201364/b201364.txt">Table of n, a(n) for n = 1..57</a>

%H Wilfrid Keller, <a href="http://www.prothsearch.com/fermat.html">Fermat factoring status</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FermatNumber.html">Fermat Number</a>

%t 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

%o (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

%Y Cf. A000215, A057775, A057778.

%K nonn

%O 1,2

%A _Arkadiusz Wesolowski_, Nov 30 2011

%E a(44)-a(50) from _Arkadiusz Wesolowski_, May 26 2023