A122028 Least positive prime primitive root of n-th prime.

3, 2, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 7, 3, 5, 2, 2, 2, 2, 7, 5, 3, 2, 3, 5, 2, 5, 2, 11, 3, 3, 2, 3, 2, 2, 7, 5, 2, 5, 2, 2, 2, 19, 5, 2, 3, 2, 3, 2, 7, 3, 7, 7, 11, 3, 5, 2, 43, 5, 3, 3, 2, 5, 17, 17, 2, 3, 19, 2, 2, 3, 7, 11, 2, 2, 5, 2, 5, 3, 29, 2, 2, 7, 5, 17, 2, 3, 13, 2, 3, 2, 13, 3, 2, 7, 5, 2, 3, 2, 2, 2

Offset: 1

Author

N. J. A. Sloane and Klaus Brockhaus, Sep 13 2006

Keywords

• nonn
• nice
• easy

References

• A. E. Western and J. C. P. Miller, Tables of Indices and Primitive Roots. Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968, p. 2.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002233 (least prime primitive root).

Programs

Maple

f:= proc(n) local p,q;
p:= ithprime(n);
q:= 2:
while numtheory:-order(q,p) <> p-1 do q:= nextprime(q) od:
q
end proc:
map(f, [$1..100]); # Robert Israel, Jan 16 2017

Mathematica

a[1] = 3; a[n_] := (p = Prime[n]; Select[Range[p], PrimeQ[#] && MultiplicativeOrder[#, p] == EulerPhi[p] &, 1]) // First; Table[a[n], {n, 100}]   (* Jean-François Alcover, Mar 30 2011 *)
a[1] = 3; a[n_] := SelectFirst[ PrimitiveRootList[ Prime[n]], PrimeQ]; Array[a, 101] (* Jean-François Alcover, Sep 28 2016 *)

Formula

a(n) = A002233(n) for n>1. - Jonathan Sondow, May 18 2017