

A214158


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


3



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
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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 JeanFrançois 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



