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%I #67 Aug 26 2022 16:54:25
%S 3,5,53,173,2083,188323,350443,350443,1014787,29861203,154363267
%N Least prime p such that the n smallest primitive roots modulo p are the first n primes.
%e a(3) = 53 because the primitive roots mod 53 are 2, 3, 5, 8, 12, 14, 18, 19, 20, 21, 22, 26, 27, ... and the 3 smallest are the first 3 primes 2, 3 and 5.
%t p=2;t=1;Do[k=2;p=NextPrime@p;While[!Xor[PrimeQ@k,MultiplicativeOrder[k,p]==p-1],k++];If[k>Prime@t,Print@p;t++;p=NextPrime[p,-1]],10^6]
%Y Cf. A213052, A350121.
%K nonn,more
%O 1,1
%A _Giorgos Kalogeropoulos_, Jul 02 2022