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

0,2

Comments

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

Links

Table of n, a(n) for n=0..53.

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)

Example

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

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 *)

Crossrefs

Cf. A046145, A046147, A023048.

Sequence in context: A091703 A004180 A011418 * A054425 A217101 A265516

Adjacent sequences: A214155 A214156 A214157 * A214159 A214160 A214161

Keyword

nonn

Author

Arkadiusz Wesolowski, Jul 05 2012

Status

approved