A319295 - OEIS

%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