|
| |
|
|
A189395
|
|
n+[ns/r]+[nt/r]; r=1, s=1/sqrt(2), t=sqrt(3).
|
|
8
|
|
|
|
2, 6, 10, 12, 16, 20, 23, 26, 30, 34, 37, 40, 44, 47, 50, 54, 58, 61, 64, 68, 71, 75, 78, 81, 85, 89, 92, 95, 99, 102, 105, 109, 113, 116, 119, 123, 127, 129, 133, 137, 140, 143, 147, 151, 153, 157, 161, 164, 167, 171, 175, 178, 181, 185, 188, 191, 195, 199, 202, 205, 209, 212, 216, 219, 222, 226, 230, 233, 236, 240, 243, 246, 250, 254, 257, 260, 264, 268, 270, 274, 278, 281, 284
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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=1/sqrt(2), t=sqrt(3) gives
a=A189395, b=A189396, c=A189397.
|
|
|
LINKS
|
Table of n, a(n) for n=1..83.
|
|
|
MATHEMATICA
|
r=1; s=2^(-1/2); t=3^(1/2);
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}] (*A189395*)
Table[b[n], {n, 1, 120}] (*A189396*)
Table[c[n], {n, 1, 120}] (*A189397*)
|
|
|
CROSSREFS
|
A189396, A189397, A189361, A189383, A189386.
Sequence in context: A195064 A055743 A189680 * A190003 A190789 A071638
Adjacent sequences: A189392 A189393 A189394 * A189396 A189397 A189398
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Clark Kimberling, Apr 21 2011
|
|
|
STATUS
|
approved
|
| |
|
|
