%I #20 Feb 11 2019 12:15:39
%S 2,29,11,269,487,653,5107,103291,40487,2544079,1093,3511,1006003
%N Smallest prime p such that there exist exactly n integers b such that 1 < b < p and b^(p-1) == 1 (mod p^2) or, equivalently, Fermat quotient q_p(b) == 0 (mod p).
%C a(n) is the smallest prime p such that A242830(PrimePi(p)) = n, PrimePi = A000720. - _Jianing Song_, Jan 27 2019
%H Richard Fischer, <a href="http://www.fermatquotient.com/FermatQuotienten/ErstBasen">Extreme first bases</a>
%e a(5) = 653 since 653 is the smallest prime with exactly five bases b = 84, 120, 197, 287, 410.
%o (PARI) first_n_entries(n)=v=vector(n); toGo=n; forprime(p=2, , count=sum(b=2, p-1, Mod(b, p^2)^(p-1)==1); if(count<=(n-1)&!v[count+1], v[count+1]=p; toGo--; if(!toGo, return(v)))) \\ _Jeppe Stig Nielsen_, Jul 31 2015, changed to include a(0) = 2 by _Jianing Song_, Feb 05 2019
%Y Cf. A001220, A130912, A248865, A242830.
%Y Subset of A134307.
%Y Cf. also A255203, A255204, A255205, A255206, A255207, A255208, A255209, A255210.
%K hard,more,nonn
%O 0,1
%A _Max Alekseyev_, Oct 24 2010
%E a(0) = 2 prepended by _Jianing Song_, Jan 27 2019
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