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A330279 Numbers k such that x^k == k (mod k + 1) has multiple solutions for 0 <= x < k. 0
27, 51, 65, 69, 75, 111, 123, 129, 147, 153, 171, 175, 185, 189, 195, 207, 231, 237, 243, 245, 267, 275, 279, 285, 291, 303, 309, 315, 321, 343, 363, 365, 369, 387, 395, 405, 411, 417, 425, 429, 435, 441, 447, 489, 495, 505, 507, 519, 531, 555, 567, 573, 591, 597 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All odd numbers have k^k == k (mod k + 1), but only some have other solutions in the least residue system (e.g. 3^27 and 19^27 == 27 (mod 28)).

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

27 is in the list because x^27 == 27 (mod 28) has three solutions: 3, 19, and 27.

MATHEMATICA

ok[k_] := Length[Select[Range[0, k-1], PowerMod[#, k, k + 1] == k &, 2]] > 1; Select[ Range@ 600, ok] (* Giovanni Resta, Dec 10 2019 *)

PROG

(PARI) isok(k) = sum(i=0, k-1, Mod(i, k+1)^k == k) > 1; \\ Michel Marcus, Dec 10 2019

CROSSREFS

Cf. A014117, A096008, A195637.

Sequence in context: A251143 A109067 A034595 * A102708 A154591 A217235

Adjacent sequences:  A330276 A330277 A330278 * A330280 A330281 A330282

KEYWORD

nonn

AUTHOR

Christopher Cormier, Dec 09 2019

STATUS

approved

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Last modified October 17 13:00 EDT 2021. Contains 348048 sequences. (Running on oeis4.)