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
Keywords
Examples
a(7) = 2 because k^7 == 0, 1, 2, 3, 4, 5, 6 (mod 7) => 2 is the smallest prime.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..16384
- Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Programs
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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 *) -
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