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%I #19 Jan 16 2023 08:08:41
%S 8,12,36,276,408,2208,2816,3168,3912,42665,44685,59973,709968,916773,
%T 1832496
%N Numbers k such that 3*2^k + 1 is a prime factor of a generalized Fermat number 7^(2^m) + 1 for some m.
%H Anders Björn and Hans Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-98-00891-6">Factors of generalized Fermat numbers</a>, Math. Comp. 67 (1998), no. 221, pp. 441-446.
%H Anders Björn and Hans Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-05-01816-8">Table errata to "Factors of generalized Fermat numbers"</a>, Math. Comp. 74 (2005), no. 252, p. 2099.
%H Anders Björn and Hans Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-10-02371-9">Table errata 2 to "Factors of generalized Fermat numbers"</a>, Math. Comp. 80 (2011), pp. 1865-1866.
%H OEIS Wiki, <a href="/wiki/Generalized_Fermat_numbers">Generalized Fermat numbers</a>
%t lst = {}; Do[p = 3*2^n + 1; If[PrimeQ[p] && IntegerQ@Log[2, MultiplicativeOrder[7, p]], AppendTo[lst, n]], {n, 3912}]; lst
%o (Magma) SetDefaultRealField(RealField(400)); IsInteger := func<k | k eq Floor(k)>; [n: n in [2..408] | IsPrime(k) and IsInteger(Log(2, Modorder(7, k))) where k is 3*2^n+1];
%Y Cf. A078304, A204620, A268657, A268658, A268659, A282944, A268660.
%Y Subsequence of A002253.
%K nonn,hard,more
%O 1,1
%A _Arkadiusz Wesolowski_, Feb 25 2017
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