A219429 Highest prime primitive root (less than p) for the n-th prime p. (or 0 if none exists).

0, 2, 3, 5, 7, 11, 11, 13, 19, 19, 17, 19, 29, 29, 43, 41, 47, 59, 61, 67, 59, 59, 79, 83, 83, 89, 101, 103, 103, 107, 109, 127, 131, 109, 139, 109, 151, 149, 163, 131, 167, 179, 181, 167, 179, 197, 191, 173, 223, 223, 227, 227, 227, 239, 251, 257, 257

Offset: 1

Author

V. Raman, Nov 19 2012

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002233 (lowest prime primitive root for the n-th prime).

Cf. A001918 (lowest primitive root for the n-th prime).

Cf. A071894 (highest primitive root (less than p) for the n-th prime p).

Programs

Maple

f:=proc(n) local p,k;
   p:= ithprime(n);
   for k from p-1 to 1 by -1 do
     if numtheory:-order(k,p) = p-1 and isprime(k) then return k fi
   od;
0
end proc;
map(f, [$1..100]); # Robert Israel, Apr 11 2021

Mathematica

Reap[For[p = 2, p<1000, p = NextPrime[p], s = Select[PrimitiveRootList[p], PrimeQ]; Sow[If[s == {}, 0, Last[s]]]]][[2, 1]] (* Jean-François Alcover, Sep 03 2016 *)

PARI

forprime(i=2,600,p=0;for(q=1,i-1,if(znorder(Mod(q,i))==eulerphi(i)&&isprime(q),p=q));print1(p","))