Note that if prime p>3 divides A001008((p+1)/2) then it also divides A001008((p3)/2).
Note that for a prime p, H([p/2]) == 2*(2^(p(p1))  1)/p^2 (mod p). Therefore a prime p divides the Wolstenholme number A001008((p+1)/2) if and only if 2^(p(p1)) == 1  p^2 (mod p^3) or, equivalently, 2^(p1) == 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)
a(6) > 5.5*10^12.  Giovanni Resta, Apr 13 2017
Primes p that are base((p1)/2) Wieferich primes, that is, primes p such that ((p1)/2)^(p1) == 1 (mod p^2).  Jianing Song, Jan 27 2019
