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

%I A201364 #29 Feb 16 2025 08:33:16
%S A201364 1,2,4,7,8,14,16,25,39,41,57,67,75,120,127,147,209,229,231,290,302,
%T A201364 320,455,547,558,747,1553,1947,2027,2458,3313,3508,4262,4727,6210,
%U A201364 6393,6539,6838,7312,8242,8557,9431,9450,12189,13252,14254,14280,15164,17909,18759
%N A201364 Numbers k such that A057775(k) is the factor of a Fermat number 2^(2^m) + 1 for some m.
%C A201364 Indices of Fermat factors in A057775.
%H A201364 Arkadiusz Wesolowski, <a href="/A201364/b201364.txt">Table of n, a(n) for n = 1..57</a>
%H A201364 Wilfrid Keller, <a href="http://www.prothsearch.com/fermat.html">Fermat factoring status</a>
%H A201364 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FermatNumber.html">Fermat Number</a>
%t A201364 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 A201364 (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 A201364 Cf. A000215, A057775, A057778.
%K A201364 nonn
%O A201364 1,2
%A A201364 _Arkadiusz Wesolowski_, Nov 30 2011
%E A201364 a(44)-a(50) from _Arkadiusz Wesolowski_, May 26 2023