1,1

A001008(n) are the Wolstenholme numbers: numerator of harmonic number H(n)=Sum_{i=1..n} 1/i. For n>0 all three listed terms {29, 37, 3373} divide both the numerator HarmonicNumber[ (p+1)/2 ] and the numerator of HarmonicNumber[ (p-3)/2 ]. Conjecture: a(n) = A121999(n) for n>0, where A121999(n) = {29, 37, 3373, ...} = Primes p such that p^2 divides Sierpinski number A014566[(p-1)/2].

A001008(n) begins {1, 3, 11, 25, 137, 49, 363, 761, 7129, 7381, 83711, 86021, 1145993, 1171733, 1195757, ...}.

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

a(2) = 29 because 29 divides both A001008(15) = 1195757 and A001008(13) = 1145993; but there is no prime p (3<p<29) that divide A001008[ (p+1)/2 ] or A001008[ (p-3)/2 ].

Cf. A001008 = Wolstenholme numbers: numerator of harmonic number H(n)=Sum_{i=1..n} 1/i. Cf. A121999 = Primes p such that p^2 divides Sierpinski number A014566[(p-1)/2]. Cf. A014566 = n^n + 1 = Sierpinski Number of the First Kind.

Sequence in context: A030274 A055062 A086174 this_sequence A106979 A087209 A072306

Adjacent sequences: A125851 A125852 A125853 this_sequence A125855 A125856 A125857

hard,more,nonn

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