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%I #22 Oct 29 2018 03:42:11
%S 1,166751,538085,601021,1078445,1579201
%N Numbers k such that k^2 + 2 divides 2^k - 2.
%C Is this sequence infinite?
%C Are there other prime terms except a(4) = 601021?
%C Let f(n) be the smallest k > 1 such that k^2 + n divides 2^k - 2. f(0) = 1093 (cf. A001220), f(1) = 95 and f(2) = a(2) = 166751.
%C The next term, if it exists, is > 10^9. - _Vaclav Kotesovec_, Oct 23 2018
%C a(7) > 1.9*10^11, if it exists. - _Giovanni Resta_, Oct 29 2018
%t Select[Range[10^7], IntegerQ[(2^# - 2) / (#^2 + 2)] &] (* _Vincenzo Librandi_, Sep 21 2018 *)
%o (PARI) isok(n) = Mod(2, n^2+2)^n==2;
%Y Cf. A001220.
%K nonn,hard,more
%O 1,2
%A _Altug Alkan_, Sep 16 2018