A033947 Smallest primitive root (in absolute value) of n-th prime.

1, -1, 2, -2, 2, 2, 3, 2, -2, 2, 3, 2, 6, 3, -2, 2, 2, 2, 2, -2, 5, -2, 2, 3, 5, 2, -2, 2, 6, 3, 3, 2, 3, 2, 2, -5, 5, 2, -2, 2, 2, 2, -2, 5, 2, -2, 2, 3, 2, 6, 3, -2, 7, -3, 3, -2, 2, -2, 5, 3, 3, 2, 5, -2, 10, 2, 3, 10, 2, 2, 3, -2, -2, 2, 2, -2, 2, 5, 3, 21, 2, 2, -5, 5, -5, 2, 3, 13, 2, -2

Offset

1,3

Comments

If there is a tie (i.e., both +k and -k are primitive roots with the least absolute value), then a(n) = +k. - Robert Israel, May 29 2026

Links

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

Maple

f:= proc(n) local p, t, k;
  p:= ithprime(n);
  t:= NumberTheory:-PrimitiveRoot(p);
  for k from 1 to t-1 do if NumberTheory:-MultiplicativeOrder(p-k, p) = p-1 then return -k fi od:
  t
end proc:
map(f, [$1..100]); # Robert Israel, May 29 2026

Crossrefs

Cf. A001918, A002199, A000040.

Sequence in context: A136164 A182860 A328830 * A069719 A385393 A316990

Adjacent sequences: A033944 A033945 A033946 * A033948 A033949 A033950

Keyword

sign

Author

Calculated by Jud McCranie

Status

approved