A189517 -id:A189517 - cp's OEIS frontend

A189515 a(n) = n + [ns] + [nt]; s=Pi/2, t=2/Pi.

2, 6, 8, 12, 15, 18, 21, 25, 28, 31, 35, 37, 41, 43, 47, 51, 53, 57, 60, 63, 66, 70, 73, 76, 79, 82, 86, 88, 92, 96, 98, 102, 105, 108, 111, 114, 118, 121, 124, 127, 131, 133, 137, 141, 143, 147, 149, 153, 156, 159, 163, 166, 169, 172, 176, 178, 182, 185, 188, 192, 194, 198, 201, 204, 208, 211, 214, 217, 220, 223, 227, 230, 233, 237, 239, 243, 246, 249, 253, 255, 259, 262, 265

Offset: 1

Clark Kimberling, Apr 23 2011

nonn

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=Pi/2, t=2/Pi gives a=A189515, b=A189516, c=A189517.

Cf. A189516, A189517.

r=1; s=Pi/2; t=2/Pi;
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}]  (*A189515*)
Table[b[n], {n, 1, 120}]  (*A189516*)
Table[c[n], {n, 1, 120}]  (*A189517*)

a(n) = n + A140758(n) + floor(2*n/Pi). - R. J. Mathar, Sep 30 2011

A189516 a(n) = n + [nr/s] + [nt/s]; r=1, s=Pi/2, t=2/Pi.

Original entry on oeis.org

1, 3, 5, 7, 10, 11, 13, 16, 17, 20, 22, 23, 26, 27, 30, 32, 33, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 61, 62, 64, 67, 68, 71, 72, 74, 77, 78, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 106, 107, 109, 112, 113, 116, 117, 119, 122, 123, 126, 128, 129, 132, 134, 136, 138, 139, 142, 144, 146, 148, 150, 152, 154, 157, 158, 161, 162, 164, 167, 168, 171

Offset: 1

Clark Kimberling, Apr 23 2011

nonn

See A189515.

Cf. A189515, A189517.

Mathematica
```
(See A189515.)
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cp's OEIS Frontend

A189515 a(n) = n + [ns] + [nt]; s=Pi/2, t=2/Pi.

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