

A290542


a(n) is the least integer k in the interval [2, sqrt(n)] such that k^n == k (mod n), or 0 if no such integer exists.


1



0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 5, 3, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, 0
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OFFSET

4,2


LINKS

Table of n, a(n) for n=4..90.


FORMULA

a(A000040(n)) = 2 for n >= 3.
a(A001567(n)) = 2 for n >= 1.
a(A006935(n)) = 2 for n >= 2.
For n >= 3, a(x) = 2*A010051(x), where x = A000040(n).


MATHEMATICA

Table[SelectFirst[Range[2, Sqrt@ n], PowerMod[#, n , n] == Mod[#, n] &] /. k_ /; MissingQ@ k > 0, {n, 4, 90}] (* Michael De Vlieger, Aug 09 2017 *)


PROG

(MAGMA) lst:=[]; for n in [4..90] do r:=Floor(Sqrt(n)); for k in [2..r] do if Modexp(k, n, n) eq k then Append(~lst, k); break; end if; if k eq r then Append(~lst, 0); end if; end for; end for; lst;
(PARI) a(n) = for (k=2, sqrtint(n), if (Mod(k, n)^n == k, return(k)); ); return (0); \\ Michel Marcus, Aug 19 2017


CROSSREFS

Cf. A010051, A290543.
Sequence in context: A069851 A197629 A198255 * A029834 A318715 A202385
Adjacent sequences: A290539 A290540 A290541 * A290543 A290544 A290545


KEYWORD

nonn


AUTHOR

Arkadiusz Wesolowski, Aug 05 2017


STATUS

approved



