A214158 Smallest number with n as least nonnegative primitive root, or 0 if no such number exists.

1, 2, 3, 4, 0, 6, 41, 22, 0, 0, 313, 118, 4111, 457, 1031, 439, 0, 262, 53173, 191, 107227, 362, 3361, 842, 533821, 0, 12391, 0, 133321, 2906, 124153, 2042, 0, 3062, 48889, 2342, 0, 7754, 55441, 19322, 1373989, 3622, 2494381, 16022, 71761, 613034, 273001, 64682, 823766851, 0, 23126821, 115982, 129361, 29642

Offset: 0

Author

Arkadiusz Wesolowski, Jul 05 2012

Keywords

• nonn

Comments

a(A001597(n)) = 0 for n > 1.

Examples

			a(7) = 22, since 22 has 7 as smallest positive primitive root and no number < 22 has 7 as smallest positive primitive root.
		

Links

• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 313
• Eric Weisstein's World of Mathematics, Primitive Root
• Robert G. Wilson v, Table of n, a(n) for n = 0..205 (contains -1 where a term has not yet been found)

Crossrefs

Cf. A046145, A046147, A023048.

Programs

Mathematica

lst2 = {}; r = 47; smallestPrimitiveRoot[n_ /; n <= 1] = 0; smallestPrimitiveRoot[n_] := Block[{pr = PrimitiveRoot[n], g}, If[! NumericQ[pr], g = 0, g = 1; While[g <= pr, If[CoprimeQ[g, n] && MultiplicativeOrder[g, n] == EulerPhi[n], Break[]]; g++]]; g]; lst1 = Union[Flatten@Table[n^i, {i, 2, Log[2, r]}, {n, 2, r^(1/i)}]]; Do[n = 2; If[MemberQ[lst1, l], AppendTo[lst2, 0], While[True, If[smallestPrimitiveRoot[n] == l, AppendTo[lst2, n]; Break[]]; n++]], {l, r}]; Prepend[lst2, 1] (* Most of the code is from Jean-François Alcover *)