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A128465
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Numbers k such that k divides the numerator of alternating Harmonic number H'((k+1)/2) = A058313((k+1)/2).
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1
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OFFSET
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1,2
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COMMENTS
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For k > 1 all 5 listed terms are primes.
The only known numbers k such that k divides the numerator of alternating Harmonic number H'((k-1)/2) = A058313((k-1)/2) are the Wieferich primes (A001220): 1093 and 3511.
An odd prime p = prime(n) belongs to this sequence iff Fermat quotient A007663(n) == A130912(n) == 2*(-1)^((p+1)/2) (mod p). - Max Alekseyev, Nov 30 2022
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LINKS
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MATHEMATICA
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f=0; Do[ f = f + (-1)^(n+1)*1/n; g = Numerator[f]; If[ IntegerQ[ g/(2n-1) ], Print[2n-1]], {n, 1, 3000} ]
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CROSSREFS
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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