A023049 Smallest prime > n having primitive root n, or 0 if no such prime exists.

2, 3, 5, 0, 7, 11, 11, 11, 0, 17, 13, 17, 19, 17, 19, 0, 23, 29, 23, 23, 23, 31, 47, 31, 0, 29, 29, 41, 41, 41, 47, 37, 43, 41, 37, 0, 59, 47, 47, 47, 47, 59, 47, 47, 47, 67, 59, 53, 0, 53, 53, 59, 71, 59, 59, 59, 67, 73, 61, 73, 67, 71, 67, 0, 71, 79, 71, 71, 71, 79, 83, 83, 83, 79

Offset

1,1

Comments

Indices of record values of a(n)-n are (1, 2, 3, 6, 10, 18, 23, 78, 102, 105, 488, 652, 925, ...). Record values of a(n)/n are 3/2, 5/3, 11/6, 47/23, ... (Is there another n with a(n) > 2n ?) - M. F. Hasler, Feb 21 2017

Links

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

Formula

a(n) = 0 iff n is a square > 1. - M. F. Hasler, Feb 21 2017

Maple

f:= proc(n) local p;
  if issqr(n) then return 0 fi;
  p:= nextprime(n);
  do
    if numtheory:-order(n, p) = p-1 then return p fi;
    p:= nextprime(p);
  od
end proc:
f(1):= 2:
map(f, [$1..100]); # Robert Israel, Feb 21 2017

Mathematica

a[n_] := For[p = 2, p <= 2 n + 1, p = NextPrime[p], If[MemberQ[ PrimitiveRootList[p], n], Return[p]]] /. Null -> 0; Array[a, 100] (* Jean-François Alcover, Mar 05 2019 *)

Prog

(PARI) A023049(n)={issquare(n)||forprime(p=n+1, , znorder(Mod(n, p))==p-1&&return(p)); (n==1)*2} \\ M. F. Hasler, Feb 21 2017

Crossrefs

See also A056619, where the primitive root may be larger than the prime, whereas in A023049 it may not be.

Cf. A377938, A377939.

Sequence in context: A079344 A096535 A126047 * A240979 A368819 A171034

Adjacent sequences: A023046 A023047 A023048 * A023050 A023051 A023052

Keyword

nonn

Author

David W. Wilson

Status

approved