A317649 Numbers whose least primitive root is an odd prime.

4, 6, 7, 10, 14, 17, 18, 22, 23, 26, 31, 34, 38, 43, 46, 47, 49, 50, 54, 58, 62, 71, 73, 74, 79, 82, 86, 89, 94, 97, 98, 103, 106, 113, 118, 122, 127, 134, 137, 142, 146, 157, 158, 162, 166, 167, 178, 191, 193, 194, 199, 202, 206, 214, 218, 223, 226, 233, 239, 241, 242, 250, 254, 257, 262, 263

Offset

1,1

Comments

The first odd number in the sequence whose square is not in the sequence is 40487.

Links

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

Example

a(3)=7 is included because the least primitive root mod 7 is 3, an odd prime.
8 is not included because there is no primitive root mod 8 (the multiplicative group mod 8 is not cyclic).
9 is not included because the least primitive root mod 9 is 2.

Maple

filter:= proc(n) local p;
  p:= numtheory:-primroot(n);
  if p = FAIL then return false fi;
  p>2 and isprime(p)
end proc:
select(filter, [$1..1000]);

Mathematica

Select[Range@ 263, If[# == {}, False, And[PrimeQ@ #, # > 2] &@ #[[1]] ] &@ PrimitiveRootList[#] &] (* Michael De Vlieger, Aug 02 2018 *)

Prog

(PARI) isok(n) = my(r=lift(znprimroot(prime(n)))); isprime(r) && (r%2); \\ Michel Marcus, Aug 04 2018

Crossrefs

Subset of A033948.

Cf. A048976.

Sequence in context: A049306 A358731 A023635 * A265036 A366506 A310652

Adjacent sequences: A317646 A317647 A317648 * A317650 A317651 A317652

Keyword

nonn

Author

Robert Israel, Aug 02 2018

Status

approved