login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056619 Smallest prime with primitive root n, or 0 if no such prime exists. 5
2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 5, 2, 3, 2, 5, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 5, 2, 3, 2, 5, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 13, 2, 5, 2, 3, 2, 5, 2, 11, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 7, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) > n/2 for n in { 2, 6, 10, 34 }. Are there any other such indices n? - M. F. Hasler, Feb 21 2017

LINKS

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

FORMULA

a(n) = 0 only for perfect squares, A000290.

a(n) = 2 for all odd n. a(n) = 0 for even squares. a(n) = 3 for n = 2 (mod 6). a(n) = 5 for n in {12, 18, 22, 28} (mod 30). - M. F. Hasler, Feb 21 2017

MAPLE

f:= proc(n) local p;

   if n::odd then return 2

   elif issqr(n) then return 0

   fi;

   p:= 3;

   do

      if numtheory:-order(n, p) = p-1 then return p fi;

      p:= nextprime(p);

   od

end proc:

map(f, [$1..100]); # Robert Israel, Feb 21 2017

MATHEMATICA

a[n_] := Module[{p}, If[OddQ[n], Return[2], If[IntegerQ[Sqrt[n]], Return[0], p = 3; While[True, If[MultiplicativeOrder[n, p] == p-1, Return[p]]; p = NextPrime[p]]]]];

Array[a, 100] (* Jean-Fran├žois Alcover, Apr 10 2019, after Robert Israel *)

PROG

(PARI) A056619(n)=forprime(p=2, n*2, gcd(n, p)==1&&znorder(Mod(n, p))==p-1&&return(p)) \\ or, more efficient:

A056619(n)=if(bittest(n, 0), 2, !issquare(n)&&forprime(p=3, n*2, gcd(n, p)==1&&znorder(Mod(n, p))==p-1&&return(p))) \\ M. F. Hasler, Feb 21 2017

CROSSREFS

Here the primitive root may be larger than the prime, whereas in A023049 it may not be.

Cf. A001122, A001913, A019334-A019421.

Sequence in context: A269735 A187038 A332260 * A324300 A323695 A303121

Adjacent sequences:  A056616 A056617 A056618 * A056620 A056621 A056622

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Aug 07 2000

EXTENSIONS

Corrected and extended by Jud McCranie, Mar 21 2002

Corrected by Robert Israel, Feb 21 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 26 11:08 EDT 2022. Contains 354086 sequences. (Running on oeis4.)