1,2

For n>1 all 5 listed terms are primes. Numbers n such that n divides the numerator of alternating Harmonic number H'((n-1)/2) = A058313((n-1)/2) are listed in A128464(n) = {1073, 3511, ...}. Both known terms of A128464(n) are the Wieferich primes A001220(n) = {1093, 3511, ...} Primes p such that p^2 divides 2^(p-1) - 1.

Eric Weisstein, Link to a section of The World of Mathematics. Harmonic Number.

f=0; Do[ f = f + (-1)^(n+1)*1/n; g = Numerator[f]; If[ IntegerQ[ g/(2n-1) ], Print[2n-1]], {n, 1, 3000} ]

Cf. A001008 = Wolstenholme numbers: numerator of harmonic number H(n)=Sum_{i=1..n} 1/i. Cf. A058313 = Numerator of the n-th alternating harmonic number H'(n). Cf. A001220 = Wieferich primes p: p^2 divides 2^(p-1) - 1. Cf. A128463, A128464, A125854, A121999.

Adjacent sequences: A128462 A128463 A128464 this_sequence A128466 A128467 A128468

Sequence in context: A073624 A025546 A109715 this_sequence A098967 A107140 A141746

hard,more,nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Mar 10 2007