A103309 Smallest prime primitive root of n that is less than n, or 0 if none exists.

0, 0, 0, 2, 3, 2, 5, 3, 0, 2, 3, 2, 0, 2, 3, 0, 0, 3, 5, 2, 0, 0, 7, 5, 0, 2, 7, 2, 0, 2, 0, 3, 0, 0, 3, 0, 0, 2, 3, 0, 0, 7, 0, 3, 0, 0, 5, 5, 0, 3, 3, 0, 0, 2, 5, 0, 0, 0, 3, 2, 0, 2, 3, 0, 0, 0, 0, 2, 0, 0, 0, 7, 0, 5, 5, 0, 0, 0, 0, 3, 0, 2, 7, 2, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 5, 3, 0, 0, 2, 0, 5, 0

Offset: 0

Author

Harry J. Smith, Jan 29 2005

Keywords

• easy
• nonn

Comments

Differs from A046145 only for indices n = 2, 41, 109, 151, 229, ...; see A103335. - Jeppe Stig Nielsen, Mar 06 2020

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• G. Martin, The Least Prime Primitive Root and the Shifted Sieve, Acta Arith. 80 (1997), no. 3, 277-288; arXiv:math/9807104 [math.NT], 1998.
• Eric Weisstein's World of Mathematics, Primitive Root.

Crossrefs

Cf. A001918, A046144, A046145, A046146, A103310, A103335.

Programs

Maple

F:= proc(n)
  local r;
  r:= numtheory:-primroot(n);
  while r::integer and not isprime(r) do
    r:= numtheory:-primroot(r,n);
  od:
  if r = FAIL then 0 else r fi
end proc:
seq(F(n),n=0..200); # Robert Israel, May 18 2015

Mathematica

a[n_] := SelectFirst[PrimitiveRootList[n], PrimeQ[#] && # < n&] /. Missing["NotFound"] -> 0;
Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Nov 15 2017 *)