Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-07-07T07:29:27.792Z Has data issue: false hasContentIssue false
  • English
  • Français

Interleaving integer sequences

Published online by Cambridge University Press:  01 August 2016

Tony Crilly
Tony Crilly*
Affiliation:
Middlesex Business School, The Burroughs, Hendon, London NW4 4BTe-mail: t.crilly@mdx.ac.uk
Get access Rights & Permissions [Opens in a new window]

Extract

Interesting algebraic and geometric results can be obtained by interleaving integer sequences term by term. To introduce this we consider how a well-known sequence can be considered as being composed of subsequences.

The standard Fibonacci sequence (Fk):

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... (1)

is defined by the recurrence relation Fk = Fk - 1 + Fk - 2 for k ≥ 3 and F1 = F2 = 1.

Type
Articles
Information
The Mathematical Gazette , Volume 91 , Issue 520 , March 2007 , pp. 27 - 33
Copyright
Copyright © The Mathematical Association 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Rajesh, V. and Leversha, Gerry, Some properties of odd terms of the Fibonacci sequence, Math. Gaz, 88 (March 2004) pp. 85–86.Google Scholar
2. Sloane, N. J. A., A handbook of integer sequences, Academic Press, New York and London (1973).Google Scholar
3. Crilly, Tony, Double sequences of positive integers, Math. Gaz. 69 (December 1985) pp. 263–271.Google Scholar
4. Tim Cross, Student Problem Corner, 2003.2, Math. Gaz. 87 (July 2003) pp. 353–354.Google Scholar
5. Dickson, L., History of the theory of numbers, vol. 2, Chelsea, New York (reprint, 1971) pp. 342, 397.Google Scholar
6. Robertson, John P., Solving the generalized Pell equation x2 - Dy2 = N, http://hometown.aol.com/jpr2718 (2004).Google Scholar