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%I #31 Nov 10 2022 21:21:52
%S 1,11,341,186787,8607491,9791567,11703131,14320387,50168819,952168003,
%T 71654478989,1328490399527
%N Numbers m that divide 6^m + 5.
%C Conjecture: For k > 1, k^m == 1 - k (mod m) has infinitely many positive solutions.
%C Also includes 11834972807906571233 = 31*381773316384082943. - _Robert Israel_, Oct 03 2019
%C a(13) > 10^15. - _Max Alekseyev_, Nov 10 2022
%t Join[{1},Select[Range[98*10^5],PowerMod[6,#,#]==#-5&]] (* The program generates the first six terms of the sequence. To generate more, increase the Range constant but the program may take a long time to run. *) (* _Harvey P. Dale_, Feb 05 2022 *)
%o (Magma) [1] cat [n: n in [1..10^8] | Modexp(6, n, n) + 5 eq n];
%Y Solutions to k^m == 1-k (mod m): A006521 (k = 2), A015973 (k = 3), A327840 (k = 4), A123047 (k = 5), this sequence (k = 6).
%Y Cf. A245318, A277288, A015891, A253209.
%K nonn,more
%O 1,2
%A _Juri-Stepan Gerasimov_, Sep 30 2019
%E a(11) from _Giovanni Resta_, Oct 02 2019
%E a(12) from _Max Alekseyev_, Nov 10 2022