%I #35 Jul 28 2016 22:35:53
%S 3,11,113
%N Smallest prime p where a base b with 1 < b < p exists such that b^(p-1) == 1 (mod p^n).
%C Smallest prime p such that A254444(i) >= n, where i is the index of p in A000040.
%C For n > 1, a(n) is a term of A134307.
%C For n > 1, if A000040(i) is a term of the sequence, then A249275(i) < A000040(i).
%C For n > 1, smallest prime p such that T(n, i) < p, where i is the index of p in A000040 and T = A257833.
%C a(4) > 5*10^8 if it exists (see Fischer link).
%H R. Fischer, <a href="http://www.fermatquotient.com/FermatQuotienten/FermatQ3.txt">Thema: Fermatquotient B^(P-1) == 1 (mod P^3)</a>.
%e For n = 3: p = 113 satisfies 68^(p-1) == 1 (mod p^3) and there is no smaller prime p such that p satisfies b^(p-1) == 1 (mod p^3) for some b with 1 < b < p, so a(3) = 113.
%o (PARI) a(n) = forprime(p=1, , for(b=2, p-1, if(Mod(b, p^n)^(p-1)==1, return(p))))
%Y Cf. A134307, A254444, A257833.
%K nonn,hard,more,bref
%O 1,1
%A _Felix Fröhlich_, Jul 28 2016