A189533 n+[ns/r]+[nt/r]; r=1, s=arcsin(3/5), t=arcsin(4/5).

1, 4, 6, 9, 12, 14, 17, 20, 22, 25, 28, 30, 33, 35, 37, 40, 42, 45, 48, 50, 53, 56, 58, 61, 64, 66, 69, 71, 73, 76, 78, 81, 84, 86, 89, 92, 94, 97, 100, 102, 105, 107, 109, 112, 114, 117, 120, 122, 125, 128, 130, 133, 136, 138, 141, 143, 145, 148, 150, 153, 156, 158, 161, 164, 166, 169, 172, 174, 176, 179, 181, 184, 186, 189, 192, 194, 197, 200, 202, 205, 208, 210, 212, 215

Offset

1,2

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=arcsin(3/5), t=arcsin(4/5) gives

a=A189533, b=A189534, c=A189535.

Links

Table of n, a(n) for n=1..84.

Mathematica

r=1; s=ArcSin[3/5]; t=ArcSin[4/5];
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];
Table[a[n], {n, 1, 120}]  (*A189533*)
Table[b[n], {n, 1, 120}]  (*A189534*)
Table[c[n], {n, 1, 120}]  (*A189535*)

Crossrefs

Cf. A189534, A189535.

Sequence in context: A066095 A003622 A330215 * A047408 A060644 A122550

Adjacent sequences: A189530 A189531 A189532 * A189534 A189535 A189536

Keyword

nonn

Author

Clark Kimberling, Apr 23 2011

Extensions

a(84) corrected by Georg Fischer, Jun 10 2020

Status

approved