1,1

Note that if prime p>3 divides A001008((p+1)/2) then it also divides A001008((p-3)/2).

Note that for a prime p, H([p/2]) == 2*(2^(-p(p-1))-1)/p^2 (mod p). Therefore a prime p divides the Wolstenholme number A001008((p+1)/2) if and only if 2^(-p(p-1)) == 1-p^2 (mod p^3) or, equivalently, 2^(p-1) == 1+p (mod p^2).

Disjunctive union of the sequences A154998 and A121999 that contain primes congruent respectively to 1,3 and 5,7 modulo 8. (Alekseyev)

No other terms below 10^11. (Alekseyev)

a(1) = 3 because prime 3 divides A001008(2) = 3 and there is no p<3 that divides A001008((p+1)/2).

a(2) = 29 because 29 divides A001008(15) = 1195757; but there is no prime p (3<p<29) that divides A001008((p+1)/2).

Cf. A001008, A121999, A014566, A154998

Adjacent sequences: A125851 A125852 A125853 this_sequence A125855 A125856 A125857

Sequence in context: A030274 A055062 A086174 this_sequence A106979 A087209 A165440

hard,more,nonn,new

Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 11 2006

Entry revised and a(5)=2001907169 provided by Max Alekseyev (maxale(AT)gmail.com), Jan 18 2009

Edited by Max Alekseyev (maxale(AT)gmail.com), Oct 13 2009