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A271267 Even numbers k such that k + 2 divides k^k + 2.

%I A271267 #30 Apr 17 2021 02:16:37
%S A271267 4,16,196,2836,5956,25936,65536,540736,598816,797476,1151536,3704416,
%T A271267 8095984,11272276,13362420,21235696,29640832,31084096,42913396,
%U A271267 49960912,55137316,70254724,70836676,81158416,94618996,111849956,129275056,150026176,168267856,169242676,189796420,192226516,198464176,208232116,244553296,246605776,300018016,318143296
%N A271267 Even numbers k such that k + 2 divides k^k + 2.
%C A271267 In other words, even numbers k such that k + 2 divides A014566(k) + 1.
%C A271267 Even terms of A213382.
%C A271267 4, 16, 65536 are the numbers of the form 2^(2^(2^k)), for k >= 0. Are there other members of this sequence with the form of 2^(2^(2^k))?
%C A271267 2^(2^(2^3)) and 2^(2^(2^4)) are terms. - _Michael S. Branicky_, Apr 16 2021
%H A271267 Michael S. Branicky, <a href="/A271267/b271267.txt">Table of n, a(n) for n = 1..150</a>
%e A271267 4 is a term because 4 + 2 = 6 divides 4^4 + 2 = 258.
%t A271267 Select[Range[2, 10^4, 2], Divisible[#^# + 2, # + 2] &] (* _Michael De Vlieger_, Apr 03 2016 *)
%o A271267 (PARI) lista(nn) = forstep(n=2, nn, 2, if( Mod(n, n+2)^n == -2 , print1(n, ", "))); \\ _Joerg Arndt_, Apr 03 2016
%o A271267 (Python)
%o A271267 def afind(limit):
%o A271267   k = 2
%o A271267   while k < limit:
%o A271267     if (pow(k, k, k+2) + 2)%(k+2) == 0: print(k, end=", ")
%o A271267     k += 2
%o A271267 afind(10**7) # _Michael S. Branicky_, Apr 16 2021
%Y A271267 Cf. A014566, A081765, A213382.
%K A271267 nonn
%O A271267 1,1
%A A271267 _Altug Alkan_, Apr 03 2016