A103310 Largest prime primitive root of n that is less than n, or 0 if none exists.

0, 0, 0, 2, 3, 3, 5, 5, 0, 5, 7, 7, 0, 11, 5, 0, 0, 11, 11, 13, 0, 0, 19, 19, 0, 23, 19, 23, 0, 19, 0, 17, 0, 0, 31, 0, 0, 19, 29, 0, 0, 29, 0, 29, 0, 0, 43, 43, 0, 47, 47, 0, 0, 41, 47, 0, 0, 0, 47, 47, 0, 59, 53, 0, 0, 0, 0, 61, 0, 0, 0, 67, 0, 59, 61, 0, 0, 0, 0, 59, 0, 59, 71, 79, 0, 0, 73

Offset

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Primitive Root.

Maple

hasproot:= proc(n)
  if n::odd then nops(numtheory:-factorset(n))=1
  else padic:-ordp(n, 2)=1 and nops(numtheory:-factorset(n/2))=1
  fi
end proc;
hasproot(2):= true: hasproot(4):= true:
f:= proc(n) local p, t;
  if not hasproot(n) then return 0 fi;
  t:= numtheory:-phi(n);
  p:= prevprime(n);
  while not numtheory:-order(p, n)=t do
    if p = 2 then return 0 fi;
    p:= prevprime(p);
  od;
  p
end proc:
f(0):= 0: f(1):= 0: f(2):= 0:
map(f, [$0..100]); # Robert Israel, Sep 08 2020

Mathematica

a[n_] := Module[{R = PrimitiveRootList[n], s}, s = Select[R, # < n && PrimeQ[#]&]; If[s == {}, 0, s[[-1]]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 01 2023 *)

Crossrefs

Cf. A001918, A046144, A046145, A046146, A103309.

Sequence in context: A158745 A175108 A265145 * A046146 A081768 A273493

Adjacent sequences: A103307 A103308 A103309 * A103311 A103312 A103313

Keyword

easy,nonn

Author

Harry J. Smith, Jan 29 2005

Status

approved