A189399 n+[ns/r]+[nt/r]; r=1, s=sqrt(e), t=e.

4, 10, 15, 20, 26, 31, 37, 42, 47, 53, 58, 63, 69, 75, 79, 85, 91, 95, 101, 106, 112, 117, 122, 128, 133, 138, 144, 150, 154, 160, 166, 170, 176, 182, 187, 192, 198, 203, 209, 213, 219, 225, 229, 235, 241, 246, 251, 257, 262, 267, 273, 278, 284, 289, 294, 300, 304, 310, 316, 321, 326, 332, 337, 342, 348, 353, 359, 364, 369, 375, 380, 385, 391, 397, 401, 407, 412, 418, 423, 428, 434, 439

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=sqrt(e), t=e gives

a=A189399, b=A189400, c=A189401.

Links

Table of n, a(n) for n=1..82.

Mathematica

r=1; s=E^(-1/2); t=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}]  (*A189399*)
Table[b[n], {n, 1, 120}]  (*A189400*)
Table[c[n], {n, 1, 120}]  (*A189401*)

Crossrefs

Cf. A189400, A189401, A189402.

Sequence in context: A310460 A310461 A310462 * A310463 A310464 A310465

Adjacent sequences: A189396 A189397 A189398 * A189400 A189401 A189402

Keyword

nonn

Author

Clark Kimberling, Apr 21 2011

Status

approved