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!)
A249973 Positive integers A when the positive roots of r^2 = Ar + B are listed in increasing order. 1
1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 3, 1, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 1, 2, 3, 4, 1, 2, 3, 1, 4, 2, 1, 3, 2, 4, 1, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 1, 2, 3, 4, 5, 1, 2, 3, 4, 1, 2, 5, 3, 1, 4, 2, 1, 3, 5, 2, 4, 1, 3, 2, 5, 1, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Generalize the Fibonacci sequence recurrence equation as: F_(n+1) = A*F_n + B*F_(n-1), where A and B are positive integers. As n goes to infinity, the ratio F_n / F_(n-1) approaches the positive real number r = (A + sqrt(A*A + 4B))/2. This sequence gives the A values in increasing order of r.

In case of a tie in r values, then sort in increasing order of sqrt(A*A + B*B).

This A sequence appears to be the ordinal transform of the B sequence (A249974) and vice versa. The associative arrays of A and B are transposes. The first row of A's associative array seems to be A006000.

For the A and B values leading to a positive integer limit r see a comment in A063929. - Wolfdieter Lang, Jan 12 2015

LINKS

Table of n, a(n) for n=1..78.

EXAMPLE

a(6) = 2 because the 6th smallest value of r (approximately 2.732050808) is that for A=2, B=2.

PROG

(PARI) \\ see A249974

CROSSREFS

Cf. A249974, A006000.

Sequence in context: A107450 A341765 A104248 * A343854 A069349 A167404

Adjacent sequences:  A249970 A249971 A249972 * A249974 A249975 A249976

KEYWORD

easy,nonn

AUTHOR

Kerry Mitchell, Nov 09 2014

EXTENSIONS

Edited. - Wolfdieter Lang, Jan 11 2015

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 September 23 14:40 EDT 2021. Contains 347618 sequences. (Running on oeis4.)