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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.

%I A066529 #23 Feb 16 2025 08:32:45
%S A066529 1,2,4,0,9,13,20,0,0,65,117,566,88,173,85,0,64,5426,43,10217,80,474,
%T A066529 326,44110,0,1479,0,12443,1842,11662,775,0,23559,5029,6461,0,3894,
%U A066529 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 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.
%C A066529 The corresponding primes are in A023048.
%C A066529 For n < 150, only a(108) is presently unknown. - _Robert G. Wilson v_, Jan 03 2006
%H A066529 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/p-roots.html#avg">Least prime primitive root of prime numbers</a>
%H A066529 E. Weisstein, <a href="https://mathworld.wolfram.com/PrimitiveRoot.html">Primitive Roots</a>
%H A066529 <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>
%F A066529 a(n) = 0 iff n is a perfect power (A001597) > 1. - _Robert G. Wilson v_, Jan 03 2006
%F A066529 a(n) = min { k | A001918(k) = n } U {0} = A000720(A023048(n)) (or zero). - _M. F. Hasler_, Jun 01 2018
%e A066529 a(6) = 13 because Prime[13] = 41 is the least prime with least primitive root = 6
%t A066529 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 A066529 (* 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 A066529 Cf. A001918, A001122, A001123, A023048, A001597.
%K A066529 nonn
%O A066529 1,2
%A A066529 _Wouter Meeussen_, Jan 06 2002
%E A066529 Edited by _Dean Hickerson_, Jan 14 2002
%E A066529 Further terms from _Robert G. Wilson v_, Jan 03 2006