A263984 Least composite primitive root of n-th prime.

9, 8, 8, 10, 6, 6, 6, 10, 10, 8, 12, 15, 6, 12, 10, 8, 6, 6, 12, 21, 14, 6, 6, 6, 10, 8, 6, 6, 6, 6, 6, 6, 6, 12, 8, 6, 6, 12, 10, 8, 6, 10, 21, 10, 8, 6, 22, 6, 6, 6, 6, 14, 14, 6, 6, 10, 8, 6, 6, 12, 12, 8, 14, 22, 10, 8, 28, 10, 6, 18

Offset: 1

Author

Franklin T. Adams-Watters, Oct 31 2015

Keywords

• nonn

Comments

The only square in the sequence is a(1) = 9.

It seems nearly certain that all nonsquare composite numbers occur in this sequence.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001918, A002233, A122028.

Programs

Mathematica

primrootQ[n_, r_] := MultiplicativeOrder[r, n] == EulerPhi[n];
a[n_] := Module[{p = Prime[n], k = 6}, While[PrimeQ[k] || GCD[k, p] != 1 || !primrootQ[p, k], k++]; k];
Array[a, 70] (* Jean-François Alcover, Oct 23 2020, after PARI code *)

PARI

isprimroot(n,r)=znorder(Mod(r,n))==eulerphi(n)
a(n)=my(p=prime(n),k=6);while(isprime(k)||gcd(k,p)!=1||!isprimroot(p,k),k++);k