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 A122632 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. 0
 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; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS 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. LINKS Table of n, a(n) for n=1..105. EXAMPLE 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. MATHEMATICA Flatten@Table[Count[Select[Union@Flatten@Outer[Divide, Range[n + 1] - 1, Range[n]] , # <= 1 &], _?(Floor[n #] == k &)], {n, 12}, {k, n}] (* Birkas Gyorgy *) CROSSREFS Cf. A002088 (row sums), A006842/A006843 (Farey fractions). Sequence in context: A083415 A115514 A326038 * A176809 A317815 A318423 Adjacent sequences: A122629 A122630 A122631 * A122633 A122634 A122635 KEYWORD nonn,tabl AUTHOR Franklin T. Adams-Watters, Oct 20 2006 STATUS approved

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Last modified September 17 03:10 EDT 2024. Contains 375984 sequences. (Running on oeis4.)