A097279 Alternating-harmonic primes.

5, 11, 23, 59, 67, 83, 89, 101, 107, 109, 127, 163, 167, 197, 229, 233, 251, 283, 311, 317, 349, 421, 491, 557, 577, 643, 673, 683, 719, 727, 761, 827, 1009, 1061, 1129, 1163, 1193, 1231, 1327, 1373

Offset

1,1

Comments

These primes, analogous to the harmonic primes in A092101, divide exactly one term of A058313, the numerators of the alternating harmonic numbers. It can be shown that for prime p > 3, if p = 6k-1, then p divides A058313(4k-1), otherwise if p = 6k+1, then p divides A058313(4k). Much of the analysis by Eswarathasan and Levine applies to alternating harmonic sums.

References

A. Eswarathasan and E. Levine, p-integral harmonic sums, Discrete Math. 91 (1991), 249-257.

Links

Table of n, a(n) for n=1..40.

Mathematica

maxPrime=1000; lst={}; Do[p=Prime[n]; cnt=0; s=0; i=1; While[s=s+(-1)^(i-1)/i; If[Mod[Numerator[s], p]==0, cnt++ ]; cnt<2&&i<p^2, i++ ]; If[cnt==1, AppendTo[lst, p]], {n, 3, PrimePi[maxPrime]}]; lst

Crossrefs

Sequence in context: A340340 A046138 A296322 * A106171 A276174 A059455

Adjacent sequences: A097276 A097277 A097278 * A097280 A097281 A097282

Keyword

hard,nonn

Author

T. D. Noe, Aug 04 2004

Status

approved