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%I #9 Jun 08 2015 04:42:20
%S 2,3,11,19,13,31,47,43,37
%N Smallest prime p for which exactly n primes k with k < p exist such that F_p-(p/k) == 0 (mod p), where F_i = A000045(i) and (a/b) denotes the Legendre symbol, or 0 if no such p exists.
%C Smallest p = prime(x) such that A257978(x) == n.
%C Conjecture: a(9) = 0 (based on observation of the asymptotic behavior of A257978).
%C a(10)-a(16) are 59, 71, 101, 97, 139, 127, 149.
%o (PARI) for(n=0, 10, forprime(p=2, , i=0; forprime(k=2, p, if(Mod(fibonacci(p-kronecker(p, k)), p)==0, i++)); if(i==n, print1(p, ", "); break({1}))))
%Y Cf. A257978.
%K nonn,more
%O 0,1
%A _Felix Fröhlich_, May 15 2015