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.

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

Offset

4,2

Links

Antti Karttunen, Table of n, a(n) for n = 4..20000

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 * A359300 A029834 A318715

Adjacent sequences: A290539 A290540 A290541 * A290543 A290544 A290545

Keyword

nonn

Author

Arkadiusz Wesolowski, Aug 05 2017

Status

approved