A263429 Smallest prime p such that binomial(2*p-1, p-1) == 1 (mod p^n), or 0 if no such p exists.

2, 3, 5, 16843

Offset: 1

Author

Felix Fröhlich, Oct 18 2015

Keywords

• nonn
• hard
• more
• bref

Comments

For n > 1, smallest p = prime(i) such that A244919(i) = n.

For n > 3, p is a term of A088164.

Conjecture: a(n) = 0 for n > 4 (McIntosh, 1995, p. 387).

Links

• R. J. McIntosh, On the converse of Wolstenholme's theorem, Acta Arithmetica, Vol. 71, No. 4 (1995), 381-389.

Crossrefs

Cf. A088164, A244919.

Programs

PARI

a(n) = my(p=2); while(Mod(binomial(2*p-1, p-1), p^n)!=1, p=nextprime(p+1)); p