A282944 - OEIS

%I #19 Jan 16 2023 08:09:09

%S 6,30,36,66,276,353,2816,3189,34350,48150,80190,1832496,2291610,

%T 5082306,10829346

%N Numbers k such that 3*2^k + 1 is a prime factor of a generalized Fermat number 11^(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[11, p]], AppendTo[lst, n]], {n, 3189}]; lst

%o (Magma) SetDefaultRealField(RealField(350)); IsInteger := func<k | k eq Floor(k)>; [n: n in [2..353] | IsPrime(k) and IsInteger(Log(2, Modorder(11, k))) where k is 3*2^n+1];

%Y Cf. A199592, A204620, A268657, A268658, A282943, A268659, A268660.

%Y Subsequence of A002253.

%K nonn,hard,more

%O 1,1

%A _Arkadiusz Wesolowski_, Feb 25 2017