A189402 n+[ns/r]+[nt/r]; r=1, s=e, t=e^2.

10, 21, 33, 43, 54, 66, 77, 88, 99, 110, 121, 132, 144, 155, 165, 177, 188, 199, 210, 221, 233, 243, 254, 266, 276, 288, 299, 310, 321, 332, 344, 354, 365, 377, 388, 399, 410, 421, 433, 443, 454, 466, 476, 488, 499, 510, 521, 532, 544, 554, 565, 577, 588, 599, 610, 621, 632, 643, 654, 666, 676, 688, 699

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^2 gives

a=A189402, b=A189403, c=A189404.

Links

Table of n, a(n) for n=1..63.

Mathematica

r=1; s=E; t=E^2;
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}]  (*A189402*)
Table[b[n], {n, 1, 120}]  (*A189403*)
Table[c[n], {n, 1, 120}]  (*A189404*)

Crossrefs

Cf. A189403, A189404, A189399.

Sequence in context: A017509 A184989 A072806 * A051942 A250664 A082581

Adjacent sequences: A189399 A189400 A189401 * A189403 A189404 A189405

Keyword

nonn

Author

Clark Kimberling, Apr 21 2011

Status

approved