A066529 a(n) is the least index such that the least primitive root of the a(n)-th prime is n, or zero if no such prime exists.

1, 2, 4, 0, 9, 13, 20, 0, 0, 65, 117, 566, 88, 173, 85, 0, 64, 5426, 43, 10217, 80, 474, 326, 44110, 0, 1479, 0, 12443, 1842, 11662, 775, 0, 23559, 5029, 6461, 0, 3894, 5629, 15177, 105242, 14401, 182683, 9204, 7103, 5518399, 23888, 24092, 42304997, 0, 1455704, 27848, 12107, 14837, 205691645, 38451, 12102037, 39370, 28902, 57481, 56379, 90901, 53468, 5918705, 0, 732055, 1738826, 242495, 265666, 10523, 388487, 260680

Offset

1,2

Comments

The corresponding primes are in A023048.

For n < 150, only a(108) is presently unknown. - Robert G. Wilson v, Jan 03 2006

Links

Table of n, a(n) for n=1..71.

Tomás Oliveira e Silva, Least prime primitive root of prime numbers

E. Weisstein, Primitive Roots

Index entries for primes by primitive root

Formula

a(n) = 0 iff n is a perfect power (A001597) > 1. - Robert G. Wilson v, Jan 03 2006

a(n) = min { k | A001918(k) = n } U {0} = A000720(A023048(n)) (or zero). - M. F. Hasler, Jun 01 2018

Example

a(6) = 13 because Prime[13] = 41 is the least prime with least primitive root = 6

Mathematica

big = Table[ p = Prime[ n ]; PrimitiveRoot[ p ], {n, 1, 1000000} ]; Flatten[ Table[ Position[ big, n, 1, 1 ]/.{}-> 0, {n, 79} ] ] (* First load package NumberTheory`NumberTheoryFunctions` *)
(* first load package *) << NumberTheory`NumberTheoryFunctions` (* then do *) t = Table[0, {100}]; Do[a = PrimitiveRoot@Prime@n; If[a < 101 && t[[a]] == 0, t[[a]] = n], {n, 10^6}]; t (* Robert G. Wilson v, Dec 15 2005 *)

Crossrefs

Cf. A001918, A001122, A001123, A023048, A001597.

Sequence in context: A338168 A180192 A369019 * A052080 A261754 A073451

Adjacent sequences: A066526 A066527 A066528 * A066530 A066531 A066532

Keyword

nonn

Author

Wouter Meeussen, Jan 06 2002

Extensions

Edited by Dean Hickerson, Jan 14 2002

Further terms from Robert G. Wilson v, Jan 03 2006

Status

approved