A233518 Primes p such that x^x == x (mod p) for some number x with 1 < x < p.

7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 61, 67, 71, 73, 79, 89, 97, 101, 103, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 181, 191, 193, 197, 199, 211, 223, 229, 233, 239, 241, 251, 257, 263, 271, 277, 281, 283, 307, 311, 313, 331, 337

Offset: 1

Author

T. D. Noe, Feb 18 2014

Keywords

• nonn

Comments

Complement of A065296.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Pär Kurlberg, Florian Luca, and Igor Shparlinski, On the fixed points of the map x -> x^x modulo a prime, arX1v 1402.4464

Crossrefs

Cf. A065295, A065296, A233519, A233520.

Programs

Mathematica

fQ[p_] := Min[Table[Mod[PowerMod[x, x, p] - x, p], {x, 2, p - 1}]] == 0; Select[Prime[Range[2, 100]], fQ[#] &]