login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A120859 Dispersion of the sequence {[r*n]+1}, where r=3+8^(1/2). 5
1, 2, 6, 3, 12, 35, 4, 18, 70, 204, 5, 24, 105, 408, 1189, 7, 30, 140, 612, 2378, 6930, 8, 41, 175, 816, 3567, 13860, 40391, 9, 47, 239, 1020, 4756, 20790, 80782, 235416, 10, 53, 274, 1393, 5945, 27720, 121173, 470832, 1372105, 11, 59, 309, 1597, 8119 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Every positive integer occurs exactly once and every pair of rows are mutually interspersed. That is, beginning at the first term of any row having greater initial term than that of another row, all the following terms individually separate the individual terms of the other row.

REFERENCES

Clark Kimberling, The equation (j+k+1)^2-4*k=Q*n^2 and related dispersions, Journal of Integer Sequences 10 (2007, Article 07.2.7) 1-17.

LINKS

Table of n, a(n) for n=1..50.

N. J. A. Sloane, Classic Sequences.

FORMULA

(1) Column 1 is the sequence {[s(n-1)]+1} where 1/r+1/s=1. The numbers in all the other columns, arranged in increasing order, form the sequence {[r*n]+1}. (2) Every row satisfies these recurrences: x(n+1)=[r*x(n)]+1 and x(n+2)=6*x(n+1)-x(n).

EXAMPLE

Northwest corner:

1 6 35 204 1189

2 12 70 408 2378

3 18 105 612 4756

4 24 140 816 4348

5 30 175 1020 5945.

In row 1, we have 6=[r]+1, 35=[6r], 204=[35r]+1; each new

row starts with the least "new" number n, followed

by [nr]+1, [[nr+1]r+1], [[[nr+1]r+1]r]+1 and so on.

CROSSREFS

Cf. A120858, A120860, A120861, A120862, A120863.

Sequence in context: A207901 A054619 A054618 * A253258 A098810 A081469

Adjacent sequences:  A120856 A120857 A120858 * A120860 A120861 A120862

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jul 09 2006

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 07:56 EDT 2020. Contains 334585 sequences. (Running on oeis4.)