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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.
5
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
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
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