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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
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
Sequence in context: A067694 A131810 A365143 * A192295 A037195 A271319
KEYWORD
nonn
AUTHOR
T. D. Noe, Feb 19 2014
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)