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

1,2

Links

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

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 *)

Prog

(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", "))

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).

Sequence in context: A141792 A180458 A060264 * A256457 A104192 A290639

Adjacent sequences: A219426 A219427 A219428 * A219430 A219431 A219432

Keyword

nonn

Author

V. Raman, Nov 19 2012

Status

approved