A319295 Numbers k such that k^2 + 2 divides 2^k - 2.

1, 166751, 538085, 601021, 1078445, 1579201

Offset

1,2

Comments

Is this sequence infinite?

Are there other prime terms except a(4) = 601021?

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.

The next term, if it exists, is > 10^9. - Vaclav Kotesovec, Oct 23 2018

a(7) > 1.9*10^11, if it exists. - Giovanni Resta, Oct 29 2018

Links

Table of n, a(n) for n=1..6.

Mathematica

Select[Range[10^7], IntegerQ[(2^# - 2) / (#^2 + 2)] &] (* Vincenzo Librandi, Sep 21 2018 *)

Prog

(PARI) isok(n) = Mod(2, n^2+2)^n==2;

Crossrefs

Cf. A001220.

Sequence in context: A186919 A185803 A250931 * A235846 A187170 A047829

Adjacent sequences: A319292 A319293 A319294 * A319296 A319297 A319298

Keyword

nonn,hard,more

Author

Altug Alkan, Sep 16 2018

Status

approved