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A103309 Smallest prime primitive root of n that is less than n, or 0 if none exists. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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.

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-Fran├žois Alcover, Nov 15 2017 *)

CROSSREFS

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

Sequence in context: A005731 A132962 A046145 * A248207 A174621 A007967

Adjacent sequences:  A103306 A103307 A103308 * A103310 A103311 A103312

KEYWORD

easy,nonn

AUTHOR

Harry J. Smith, Jan 29 2005

STATUS

approved

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)