A114977 Numbers k such that (j^k + k^j) == 0 (mod k+j), j=2 case.

1, 2, 8, 128, 2144, 4808, 12872, 14168, 32377, 33672, 45992, 116192, 185768, 186824, 271208, 426008, 484177, 524288, 601352, 612768, 755792, 996032, 1878368, 2262752, 3094247, 4325960, 4810808, 6331808, 6707352, 10037792, 10908137, 11475128, 12672992, 13705232

Offset: 1

Author

Zak Seidov, Feb 22 2006

Keywords

• nonn

Comments

From Robert G. Wilson v, Aug 02 2021: (Start)

Prime terms: 2, then A156048.

The exponents of the powers of two which are terms: 0, 1, then A014741(n)+1.

The vast majority of terms are congruent to 8 (mod 24); no terms are congruent to 4 (mod 6) nor to 3 (mod 10).

(End)

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1189 (first 645 terms from Hiroaki Yamanouchi).

Crossrefs

Cf. A156038 (odd terms), A156048 (odd prime terms).

Cf. A014741, A114978, A114979, A114980, A114981.

Programs

Mathematica

fQ[n_] := PowerMod[2, n, n + 2] + 2 == n; Select[ Range[10^7], fQ] (* Robert G. Wilson v, Aug 02 2021 *)

PARI

isok(n, k=2) = (k^n+n^k) % (n+k) == 0; \\ Michel Marcus, Oct 10 2013

PARI

is(n)=Mod(2, n+2)^n==-4 \\ Charles R Greathouse IV, Oct 19 2013

Extensions

a(9)-a(22) from Michel Marcus, Oct 10 2013

a(23)-a(34) from Hiroaki Yamanouchi, Sep 26 2015