A202036 Smallest prime residue of x^n (mod n) for x=0..n-1, or 0 if no such prime exists.

0, 0, 2, 0, 2, 3, 2, 0, 0, 5, 2, 0, 2, 2, 2, 0, 2, 0, 2, 5, 7, 3, 2, 0, 7, 3, 0, 0, 2, 19, 2, 0, 2, 2, 2, 0, 2, 5, 5, 0, 2, 7, 2, 5, 17, 2, 2, 0, 19, 0, 2, 13, 2, 0, 11, 0, 7, 5, 2, 0, 2, 2, 0, 0, 2, 3, 2, 13, 2, 11, 2, 0, 2, 3, 7, 5, 2, 13, 2, 0, 0, 2, 2, 0

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Example

a(7) = 2 because k^7 == 0, 1, 2, 3, 4, 5, 6 (mod 7) => 2 is the smallest prime.

Maple

for n from 1 to 100 do: W:={}:for k from 0 to n-1 do:z:= irem(k^n, n): if type(z, prime)=true then W:=W union {z}:else fi:od: x:=nops(W): if x<>0 then printf(`%d, `, W[1]): else printf(`%d, `, 0):fi: od:

Mathematica

Table[SelectFirst[Sort[PowerMod[Range[n-1], n, n]], PrimeQ], {n, 90}]/.Missing["NotFound"]->0 (* Harvey P. Dale, May 01 2023 *)

Prog

(PARI) A202036(n) = { my(z, y=n); for(x=1, n-1, z = lift(Mod(x, n)^n); if(isprime(z), y = min(z, y))); if(y==n, 0, y); }; \\ - Antti Karttunen, May 19 2021

Crossrefs

Cf. A195812, A196082, A202034, A202035.

Sequence in context: A062244 A169979 A079957 * A246752 A246650 A264940

Adjacent sequences: A202033 A202034 A202035 * A202037 A202038 A202039

Keyword

nonn

Author

Michel Lagneau, Dec 09 2011

Status

approved