A128125 Numbers k such that 2^k == 14 (mod k).

1, 2, 3, 10, 1010, 61610, 469730, 2037190, 3820821, 9227438, 21728810, 24372562, 207034456857, 1957657325241, 2002159320610, 35169368880130, 36496347203230, 116800477091426

Offset: 1

Author

Alexander Adamchuk, Feb 15 2007

Keywords

• hard
• more
• nonn

Comments

No other terms below 10^15. Some larger terms: 279283702428813463, 3075304070192893442, 21894426987819404424310, 4616079845508388554313022889, 82759461944940747300611642693066719359651817521, 446*(2^445-7)/1061319625781480182060453906975 (107 digits). - Max Alekseyev, Oct 03 2016

Links

• Joe K. Crump, 2^n mod n

Crossrefs

Cf. A015910, A036236, A050259 (numbers k such that 2^k == 3 (mod k)), A033981, A051447, A033982, A051446, A033983, A128121, A128122, A128123, A128124, A128126.

Programs

Mathematica

For[n=1, n<= 10^6, n++, If[PowerMod[2,n,n] == Mod[14,n], Print[n]]] (* Stefan Steinerberger, May 05 2007 *)
m = 14; Join[Select[Range[m], Divisible[2^# - m, #] &],
Select[Range[m + 1, 10^6], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 08 2018 *)

Extensions

1, 2, 3 and 10 added by N. J. A. Sloane, Apr 23 2007

More terms from Stefan Steinerberger, May 05 2007

a(13) from Max Alekseyev, May 15 2011

a(14), a(16), a(17) from Max Alekseyev, Dec 16 2013

a(15), a(18) from Max Alekseyev, Oct 03 2016