A066529 - OEIS

%I #22 Nov 05 2018 14:34:26

%S 1,2,4,0,9,13,20,0,0,65,117,566,88,173,85,0,64,5426,43,10217,80,474,

%T 326,44110,0,1479,0,12443,1842,11662,775,0,23559,5029,6461,0,3894,

%U 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

%N 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.

%C The corresponding primes are in A023048.

%C For n < 150, only a(108) is presently unknown. - _Robert G. Wilson v_, Jan 03 2006

%H Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/p-roots.html#avg">Least prime primitive root of prime numbers</a>

%H E. Weisstein, <a href="http://mathworld.wolfram.com/PrimitiveRoot.html">Primitive Roots</a>

%H <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>

%F a(n) = 0 iff n is a perfect power (A001597) > 1. - _Robert G. Wilson v_, Jan 03 2006

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

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

%t 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` *)

%t (* 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 *)

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

%K nonn

%O 1,2

%A _Wouter Meeussen_, Jan 06 2002

%E Edited by _Dean Hickerson_, Jan 14 2002

%E Further terms from _Robert G. Wilson v_, Jan 03 2006