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A097279
Alternating-harmonic primes.
0
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.
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
KEYWORD
hard,nonn
AUTHOR
T. D. Noe, Aug 04 2004
STATUS
approved