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Search: id:A091656
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| A091656 |
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Least number k such that the continued fraction expansion of H(k) contains the numbers 1, 2, ..., n, where H(k) is the k-th Harmonic number. |
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+0
2
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| 1, 2, 5, 9, 9, 13, 26, 63, 68, 68, 68, 87, 121, 121, 165, 207, 207, 221, 221, 287, 289, 325, 428, 440, 483, 544, 544, 544, 544, 544, 558, 558, 558, 966, 1035, 1035, 1146, 1146, 1332, 1332, 1332, 1665, 1665, 1665, 1665, 1665, 1727, 1727, 2052, 2157, 2331, 2331
(list; graph; listen)
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OFFSET
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1,2
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EXAMPLE
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a(6) = 13 because CF( H(13)) = 3 + [5, 1, 1, 4, 2, 1, 3, 2, 1, 3, 1, 4, 1, 6], the first six integers are present.
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MATHEMATICA
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f[n_] := Block[{k = 1}, While[ StringPosition[ ToString[ Union[ ContinuedFraction[ Sum[1/i, {i, 1, k}]]]], StringDrop[ ToString[ Table[i, {i, n}]], -1]] == {}, k++ ]; k]; Table[ f[n], {n, 1, 52}]
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CROSSREFS
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Cf. A055573, A091655.
Sequence in context: A111290 A129140 A002580 this_sequence A133508 A125969 A070240
Adjacent sequences: A091653 A091654 A091655 this_sequence A091657 A091658 A091659
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 26 2004
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