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 A327943 Numbers m that divide 6^m + 5. 6
 1, 11, 341, 186787, 8607491, 9791567, 11703131, 14320387, 50168819, 952168003, 71654478989, 1328490399527 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: For k > 1, k^m == 1 - k (mod m) has infinitely many positive solutions. Also includes 11834972807906571233 = 31*381773316384082943. - Robert Israel, Oct 03 2019 a(13) > 10^15. - Max Alekseyev, Nov 10 2022 LINKS Table of n, a(n) for n=1..12. MATHEMATICA 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 *) PROG (Magma) [1] cat [n: n in [1..10^8] | Modexp(6, n, n) + 5 eq n]; CROSSREFS Solutions to k^m == 1-k (mod m): A006521 (k = 2), A015973 (k = 3), A327840 (k = 4), A123047 (k = 5), this sequence (k = 6). Cf. A245318, A277288, A015891, A253209. Sequence in context: A195505 A092609 A091537 * A277348 A033517 A279238 Adjacent sequences: A327940 A327941 A327942 * A327944 A327945 A327946 KEYWORD nonn,more AUTHOR Juri-Stepan Gerasimov, Sep 30 2019 EXTENSIONS a(11) from Giovanni Resta, Oct 02 2019 a(12) from Max Alekseyev, Nov 10 2022 STATUS approved

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Last modified November 28 18:35 EST 2023. Contains 367419 sequences. (Running on oeis4.)