A189512 n+[ns/r]+[nt/r]; r=1, s=e/3, t=3/e.

2, 5, 8, 11, 14, 17, 20, 23, 26, 30, 32, 35, 38, 41, 44, 47, 50, 53, 56, 60, 63, 65, 68, 71, 74, 77, 80, 83, 87, 90, 93, 95, 98, 101, 104, 107, 110, 113, 117, 120, 123, 126, 128, 131, 134, 137, 140, 143, 147, 150, 153, 156, 159, 161, 164, 167, 170, 174, 177, 180, 183, 186, 189, 191, 194, 197, 200, 204, 207, 210, 213, 216, 219, 222, 224, 227, 230, 234, 237, 240, 243, 246, 249

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=e/3, t=3/e gives

a=A189512, b=A189513, c=A189514.

Links

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

Mathematica

r=1; s=E/3; t=3/E;
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}]  (*A189512*)
Table[b[n], {n, 1, 120}]  (*A189513*)
Table[c[n], {n, 1, 120}]  (*A189514*)

Crossrefs

Cf. A189513, A189514.

Sequence in context: A016789 A190082 A165334 * A190361 A184905 A279773

Adjacent sequences: A189509 A189510 A189511 * A189513 A189514 A189515

Keyword

nonn

Author

Clark Kimberling, Apr 23 2011

Status

approved