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A233519 The number of times x^x == x (mod prime(n)) for x in 0 < x < prime(n). 4
1, 1, 1, 2, 1, 2, 3, 2, 2, 2, 3, 2, 5, 3, 2, 1, 1, 4, 3, 2, 5, 4, 1, 4, 5, 3, 4, 1, 2, 5, 5, 3, 5, 4, 2, 5, 7, 3, 2, 2, 1, 5, 3, 9, 3, 7, 6, 2, 1, 2, 6, 3, 8, 5, 5, 2, 1, 8, 3, 10, 2, 1, 8, 6, 9, 1, 9, 12, 1, 5, 5, 2, 4, 6, 6, 2, 1, 4, 5, 9, 4, 4, 3, 6, 4, 5, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This is A065295 restricted to the primes. The plot is significantly different.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Pär Kurlberg, Florian Luca, and Igor Shparlinski On the fixed points of the map x -> x^x modulo a prime arX1v 1402.4464

MATHEMATICA

f[p_] := Module[{x = Range[p - 1]}, Count[PowerMod[x, x, p] - x, 0]]; Table[f[n], {n, Prime[Range[100]]}]

CROSSREFS

Cf. A065295, A233518, A233520.

Sequence in context: A331084 A067694 A131810 * A192295 A037195 A271319

Adjacent sequences:  A233516 A233517 A233518 * A233520 A233521 A233522

KEYWORD

nonn

AUTHOR

T. D. Noe, Feb 19 2014

STATUS

approved

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Last modified September 25 16:45 EDT 2020. Contains 337344 sequences. (Running on oeis4.)