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%I #10 Oct 31 2015 14:54:05
%S 2,3,5,16843
%N Smallest prime p such that binomial(2*p-1, p-1) == 1 (mod p^n), or 0 if no such p exists.
%C For n > 1, smallest p = prime(i) such that A244919(i) = n.
%C For n > 3, p is a term of A088164.
%C Conjecture: a(n) = 0 for n > 4 (McIntosh, 1995, p. 387).
%H R. J. McIntosh, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa71/aa7144.pdf">On the converse of Wolstenholme's theorem</a>, Acta Arithmetica, Vol. 71, No. 4 (1995), 381-389.
%o (PARI) a(n) = my(p=2); while(Mod(binomial(2*p-1, p-1), p^n)!=1, p=nextprime(p+1)); p
%Y Cf. A088164, A244919.
%K nonn,hard,more,bref
%O 1,1
%A _Felix Fröhlich_, Oct 18 2015