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Search: id:A119955
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| A119955 |
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Numbers n such that denominator of n-th Harmonic Number equals denominator of n-th Alternative Harmonic Number. |
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+0
4
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| 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 27, 49, 50, 51, 52, 53, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 289, 290, 291, 292, 293, 841, 842, 843, 844
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Up to n=14 A002805[n] coincides with A058312[n]. a(n) up to a(12)=27 coincides with A096304[n].
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Harmonic Number.
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EXAMPLE
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Denominators of Harmonic Number (H[n] = Sum[1/i, {i, n}]) are A002805[n] = {1,2,6,12,60,20,140,280,2520,2520,27720,27720,360360,360360,360360,...}.
Denominators of Alternative Harmonic Number (H'[n] = Sum[(-1)^(i+1)*1/i, {i, n}]) are A058312[n] = {1,2,6,12,60,60,420,840,2520,2520,27720,27720,360360,360360,72072,...}.
a(1) = 1 because A002805[1] = A058312[1].
15 is not in a(n) because A002805[15] = 360360 is not equal to A058312[15] = 72072.
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MATHEMATICA
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Do[s1=Denominator[Sum[(-1)^(i+1)*1/i, {i, n}]]; s2=Denominator[Sum[1/i, {i, n}]]; If[Equal[s2, s1], Print[n]], {n, 1, 1500}]
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CROSSREFS
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Cf. A002805, A058312, A096304.
Sequence in context: A068585 A037472 A096304 this_sequence A158573 A047603 A047362
Adjacent sequences: A119952 A119953 A119954 this_sequence A119956 A119957 A119958
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 02 2006
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