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A097279
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Alternating-harmonic primes.
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0
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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
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OFFSET
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1,1
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COMMENTS
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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.
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REFERENCES
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A. Eswarathasan and E. Levine, p-integral harmonic sums, Discrete Math. 91 (1991), 249-257.
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LINKS
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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hard,nonn
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AUTHOR
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STATUS
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approved
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