%I #22 Sep 11 2025 03:03:30

%S 209,44685,157169,303093,362765,916773,2145353

%N Numbers k such that 3*2^k + 1 is a prime factor of a generalized Fermat number 10^(2^m) + 1 for some m.

%C Number k from A002253 is a term iff 10 is a cubic residue modulo prime p = 3*2^k + 1, that is, 10^(2^k) == 1 (mod p). - _Max Alekseyev_, Sep 06 2025

%D Wilfrid Keller, private communication, 2008.

%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 C. K. Caldwell, Top Twenty page, <a href="https://t5k.org/top20/page.php?id=10">Generalized Fermat Divisors (base=10)</a>

%H OEIS Wiki, <a href="/wiki/Generalized_Fermat_numbers">Generalized Fermat numbers</a>

%Y Subsequence of A002253.

%Y Cf. A080176, A268657, A268658, A204620, A268660, A268661, A268662, A268663, A226366, A268664.

%K nonn,hard,more

%O 1,1

%A _Arkadiusz Wesolowski_, Feb 10 2016