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!)
A120863 Fixed-k dispersion for Q=13. 5
1, 2, 13, 3, 23, 142, 4, 33, 251, 1549, 5, 46, 360, 2738, 16897, 6, 56, 502, 3927, 29867, 184318, 7, 66, 611, 5476, 42837 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For each positive integer n, there exists a unique pair (j,k) of positive integers such that (j+k+1)^2 - 4*k = 13*n^2; in fact, j(n)=A120869(n), k(n)=A120870(n). Suppose g>=1 and let k=k(g). The numbers in row g of D are among those n for which (j+k+1)^2 - 4*k = 13*n^2 for some j; that is, k stays fixed and j and n vary - hence the name "fixed-k dispersion". (The fixed-j dispersion for Q=13 is A120862.) Every positive integer occurs exactly once in D 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..26.

N. J. A. Sloane, Classic Sequences.

FORMULA

Define f(n)=11*n-3*Floor(n*F)+3, where F is the fractional part of (1+sqrt(13))*n/2. Let D(g,h) be the term in row g, column h of the array to be defined: D(1,1)=1; D(1,2)=f(1); D(1,h)=11*D(1,h-1)-D(1,h-2) for h>=3. For arbitrary g>=1, once row g is defined, define D(g+1,1)=least positive integer not in rows 1,2,...,g; D(g+1,2)=f(D(g+1,1)); D(g+1,h)=11*D(g+1,h-1)-D(g+1,h) for h>=3. All rows after row 1 are thus inductively defined.

EXAMPLE

Northwest corner:

1 13 142 1549

2 23 251 2738

3 33 360 3927

4 46 502 5476

CROSSREFS

Cf. A120858, A120859, A120860, A120861, A120862, A120869, A120870.

Sequence in context: A249224 A217010 A091023 * A286459 A093079 A095417

Adjacent sequences:  A120860 A120861 A120862 * A120864 A120865 A120866

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 31 00:53 EDT 2020. Contains 334747 sequences. (Running on oeis4.)