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Smallest prime p such that the least positive primitive root of p equals prime(n).
1

%I #27 Aug 22 2024 21:03:38

%S 3,7,23,71,643,457,311,191,2161,15791,5881,36721,156601,95471,275641,

%T 161831,712321,1171921,3384481,3659401,760321,7510801,16889161,

%U 6366361,17551561,29418841,49443241,33358081,67992961,90441961,184254841

%N Smallest prime p such that the least positive primitive root of p equals prime(n).

%C Smallest prime(m) such that A001918(m) = prime(n). (Corrected by _Jonathan Sondow_, Feb 03 2013)

%C a(36) = 831143041 and a(34) and a(35) > 1065000000. - _Robert G. Wilson v_, Jul 03 2003

%F a(n) = A023048(prime(n)). - _R. J. Mathar_, Aug 03 2018

%t << NumberTheory`NumberTheoryFunctions`; a = Table[ 0, {36}]; p = 2; Do[p = NextPrime[p]; pr = PrimitiveRoot[p]; If[ PrimeQ[pr] && PrimePi[pr] < 37 && a[[ PrimePi[pr]]] == 0, a[[ PrimePi[ pr]]] = p], {n, 2, 54000000}]; a

%o (PARI) a(n)=if(n<0,0,s=1; while(prime(n)!=lift(znprimroot(prime(s))),s++); prime(s))

%Y Cf. A001918, A023048, A066529, A084739.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Feb 02 2003

%E More terms from _Robert G. Wilson v_, Jul 03 2003