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

Author

T. D. Noe, Aug 04 2004

Keywords

• hard
• nonn

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.

Programs

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