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Search: id:A122632
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| A122632 |
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Table T(n,k) = number of initial segments of Beatty sequences for numbers > 1 of length k, cutting sequence so that all terms are < n. |
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+0
1
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| 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 3, 2, 2, 3, 1, 1, 4, 3, 2, 3, 4, 1, 1, 4, 3, 3, 3, 3, 4, 1, 1, 5, 3, 4, 2, 4, 3, 5, 1, 1, 5, 4, 3, 3, 3, 3, 4, 5, 1, 1, 6, 4, 4, 5, 2, 5, 4, 4, 6, 1, 1, 6, 4, 4, 4, 4, 4, 4, 4, 4, 6, 1, 1, 7, 5, 5, 4, 6, 2, 6, 4, 5, 5, 7, 1, 1, 7, 5, 5, 4, 6, 4, 4, 6, 4, 5, 5, 7, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Enumerate all rational numbers q in [0,1) with denominator <= n. T(n,k) is the number of these with floor(n*q) = k-1. Problem suggested by David W. Wilson.
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EXAMPLE
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T(6,3) = 2; the sequences for n=6, k=3 are 0,2,4 and 0,2,5. The sequence 0,1,3 is not counted because the next term of a Beatty sequence beginning 0,1,3 must be 4 or 5, so 0,1,3 is not a Beatty sequence truncated to numbers less than 6.
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CROSSREFS
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Cf. A002088 (row sums), A006842/A006843 (Farey fractions).
Sequence in context: A102523 A083415 A115514 this_sequence A134542 A106254 A117147
Adjacent sequences: A122629 A122630 A122631 this_sequence A122633 A122634 A122635
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KEYWORD
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nonn,tabl
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 20 2006
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