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%I #26 Jun 29 2024 16:56:07
%S 1,7,16387,4509253,24265177,42673920001,103949349763,12939780075073
%N Numbers m that divide 4^m + 3.
%C Number of solutions < 10^9 to k^n == k-1 (mod n): 1 (if k = 1), 188 (if k = 2, see A006521), 5 (if k = 3, see A015973), 5 (if k = 4, see this sequence), 5 (if k = 5), 10 (if k = 6), 10 (if k = 7), 7 (if k = 8), 5 (if k = 9), 8 (if k = 10), 11 (if k = 11), 8 (if k = 12), 9 (if k = 13), 4 (if k = 14), 3 (if k = 15), 6 (if k = 16), 7 (if k = 17), 7 (if k = 18), ...
%C a(9) > 10^15. - _Max Alekseyev_, Nov 10 2022
%t Select[Range[10^7], IntegerQ[(PowerMod[4, #, # ]+3)/# ]&] (* _Metin Sariyar_, Sep 28 2019 *)
%o (Magma) [1] cat [n: n in [1..10^8] | Modexp(4,n,n) + 3 eq n];
%o (PARI) is(n)=Mod(4,n)^n==-3 \\ _Charles R Greathouse IV_, Sep 29 2019
%Y Solutions to k^n == 1-k (mod n): A006521 (k = 2), A015973 (k = 3), this sequence (k = 4), A123047 (k = 5), A327943 (k = 6).
%Y Solutions to 4^n == k (mod n): A000079 (k = 0), A015950 (k = -1), A014945 (k = 1), A130421 (k = 2), this sequence (k = -3), A130422 (k = 3).
%Y Cf. A015940, A253208.
%K nonn,more
%O 1,2
%A _Juri-Stepan Gerasimov_, Sep 27 2019
%E a(6)-a(7) from _Giovanni Resta_, Sep 29 2019
%E a(8) from _Max Alekseyev_, Nov 10 2022
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