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

%I A114977 #40 Aug 31 2021 02:36:28
%S A114977 1,2,8,128,2144,4808,12872,14168,32377,33672,45992,116192,185768,
%T A114977 186824,271208,426008,484177,524288,601352,612768,755792,996032,
%U A114977 1878368,2262752,3094247,4325960,4810808,6331808,6707352,10037792,10908137,11475128,12672992,13705232
%N A114977 Numbers k such that (j^k + k^j) == 0 (mod k+j), j=2 case.
%C A114977 From _Robert G. Wilson v_, Aug 02 2021: (Start)
%C A114977 Prime terms: 2, then A156048.
%C A114977 The exponents of the powers of two which are terms: 0, 1, then A014741(n)+1.
%C A114977 The vast majority of terms are congruent to 8 (mod 24); no terms are congruent to 4 (mod 6) nor to 3 (mod 10).
%C A114977 (End)
%H A114977 Robert G. Wilson v, <a href="/A114977/b114977.txt">Table of n, a(n) for n = 1..1189</a> (first 645 terms from Hiroaki Yamanouchi).
%t A114977 fQ[n_] := PowerMod[2, n, n + 2] + 2 == n; Select[ Range[10^7], fQ] (* _Robert G. Wilson v_, Aug 02 2021 *)
%o A114977 (PARI) isok(n, k=2) = (k^n+n^k) % (n+k) == 0; \\ _Michel Marcus_, Oct 10 2013
%o A114977 (PARI) is(n)=Mod(2, n+2)^n==-4 \\ _Charles R Greathouse IV_, Oct 19 2013
%Y A114977 Cf. A156038 (odd terms), A156048 (odd prime terms).
%Y A114977 Cf. A014741, A114978, A114979, A114980, A114981.
%K A114977 nonn
%O A114977 1,2
%A A114977 _Zak Seidov_, Feb 22 2006
%E A114977 a(9)-a(22) from _Michel Marcus_, Oct 10 2013
%E A114977 a(23)-a(34) from _Hiroaki Yamanouchi_, Sep 26 2015