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A023049 Smallest prime > n having primitive root n, or 0 if no such prime exists. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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.

Sequence in context: A079344 A096535 A126047 * A240979 A171034 A062007

Adjacent sequences:  A023046 A023047 A023048 * A023050 A023051 A023052

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified April 25 12:36 EDT 2019. Contains 322456 sequences. (Running on oeis4.)