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A065454
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Let the k-th harmonic number be H(k) = Sum_{i=1..k} 1/i = P(k)/Q(k) = A001008(k)/A002805(k); sequence gives values of k such that Q(k) = Q(k+1).
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2
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9, 11, 13, 14, 21, 25, 27, 29, 33, 34, 35, 37, 38, 39, 44, 45, 47, 49, 50, 51, 54, 55, 56, 57, 59, 61, 64, 67, 69, 73, 74, 75, 77, 79, 81, 83, 84, 85, 86, 89, 90, 91, 92, 93, 94, 95, 97, 98, 101, 103, 105, 107, 110, 111, 113, 114, 115, 116, 117, 118, 121, 122, 123, 125
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OFFSET
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1,1
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COMMENTS
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Shiu (2016) proved that this sequence is infinite. Wu and Chen (2019) proved that the asymptotic density of this sequence is 1. - Amiram Eldar, Jan 29 2021
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LINKS
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EXAMPLE
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For example: H(11) = 83711/27720, H(12) = 86021/27720 and so a(2) = 11.
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MATHEMATICA
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Position[Partition[Denominator @ HarmonicNumber[Range[126]], 2, 1], {x_, x_}] // Flatten (* Amiram Eldar, Jan 29 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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