A355016 Least prime p such that the n smallest primitive roots modulo p are the first n primes.
3, 5, 53, 173, 2083, 188323, 350443, 350443, 1014787, 29861203, 154363267
Offset: 1
Examples
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.
Programs
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Mathematica
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]