A189530 - OEIS

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A189530

n+[ns/r]+[nt/r]; r=1, s=2^(1/3), t=2^(2/3).

3, 7, 10, 15, 18, 22, 26, 30, 34, 37, 41, 46, 49, 53, 56, 61, 64, 68, 72, 76, 80, 83, 87, 92, 95, 99, 103, 107, 111, 114, 119, 122, 126, 129, 134, 138, 141, 145, 149, 153, 157, 160, 165, 168, 172, 176, 180, 184, 187, 191, 195, 199, 203, 207, 211, 214, 218, 223, 226, 230, 233, 238, 242, 245, 249, 253, 257, 260, 264, 269, 272, 276, 279, 284, 288, 291, 296, 299, 303, 306, 311, 315, 318

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OFFSET

1,1

COMMENTS

This is one of three sequences that partition the positive integers. In general, suppose that r, s, t are positive real numbers for which the sets {i/r: i>=1}, {j/s: j>=1}, {k/t: k>=1} are pairwise disjoint. Let a(n) be the rank of n/r when all the numbers in the three sets are jointly ranked. Define b(n) and c(n) as the ranks of n/s and n/t. It is easy to prove that

a(n)=n+[ns/r]+[nt/r],

b(n)=n+[nr/s]+[nt/s],

c(n)=n+[nr/t]+[ns/t], where []=floor.

Taking r=1, s=2^(1/3), t=2^(2/3) gives

a=A189530, b=A189531, c=A189532.

LINKS

Table of n, a(n) for n=1..83.

MATHEMATICA

r=1; s=2^(1/3); t=2^(2/3);

a[n_] := n + Floor[n*s/r] + Floor[n*t/r];

b[n_] := n + Floor[n*r/s] + Floor[n*t/s];

c[n_] := n + Floor[n*r/t] + Floor[n*s/t];