login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A189460 n+[ns/r]+[nt/r]; r=2, s=sqrt(5), t=1+sqrt(5). 3
3, 7, 10, 14, 18, 21, 25, 28, 33, 37, 40, 44, 48, 51, 55, 58, 63, 67, 70, 74, 77, 81, 85, 88, 92, 97, 100, 104, 107, 111, 115, 118, 122, 127, 130, 134, 137, 141, 145, 148, 152, 155, 160, 164, 167, 171, 175, 178, 182, 185, 190, 194, 197, 201, 204, 208, 212, 215, 219, 224, 227, 231, 234, 238, 242, 245, 249, 254, 257, 261, 264, 268, 272, 275, 279, 282, 287, 291, 294, 298, 302, 305, 309 (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=2, s=sqrt(5), t=1+sqrt(5) gives

a=A189460, b=A189461, c=A189462.

LINKS

Ivan Panchenko, Table of n, a(n) for n = 1..10000

MATHEMATICA

r=2; s=5^(1/2); t=1+5^(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}]  (*A189460*)

Table[b[n], {n, 1, 120}]  (*A189461*)

Table[c[n], {n, 1, 120}]  (*A189462*)

CROSSREFS

Cf. A189461, A189462.

Sequence in context: A189999 A171983 A003231 * A172323 A190080 A184812

Adjacent sequences:  A189457 A189458 A189459 * A189461 A189462 A189463

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 22 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 26 15:27 EDT 2017. Contains 292531 sequences.