A385723 Numbers k such that m^m == m (mod k) where m = ceiling(k/2).

1, 2, 6, 7, 10, 14, 17, 18, 22, 23, 26, 30, 31, 34, 38, 41, 42, 46, 47, 50, 54, 58, 62, 66, 70, 71, 73, 74, 78, 79, 82, 86, 89, 90, 94, 97, 98, 102, 103, 106, 110, 113, 114, 118, 122, 126, 127, 130, 134, 137, 138, 142, 146, 150, 151, 154, 158, 162, 166, 167, 170

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Maple

q:= k-> (m-> 0=m&^m-m mod k)(ceil(k/2)):
select(q, [$1..200])[];  # Alois P. Heinz, Jul 08 2025

Mathematica

m[k_]:=Ceiling[k/2]; Select[Range[170], PowerMod[m[#], m[#], #]==Mod[m[#], #] &] (* Stefano Spezia, Jul 08 2025 *)

Prog

(Magma) [k: k in [1..200] | Modexp(m, m, k) eq m mod k where m is Ceiling(k/2)];
(PARI) isok(k) = my(m=ceil(k/2)); m == Mod(m, k)^m; \\ Michel Marcus, Jul 08 2025

Crossrefs

Superset of A001132 and A016825.

Cf. A004526.

Sequence in context: A061943 A029507 A047552 * A287453 A287449 A287688

Adjacent sequences: A385720 A385721 A385722 * A385724 A385725 A385726

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 07 2025

Status

approved