臺灣博碩士論文加值系統

Integer sequences have been collected by Neil Sloane since he was a graduate
student in 1965. The integer sequences database was at first stored on file cards, which
were later transferred to computer punched cards. Until year 1996 the database of the
sequences had reached 16,000 records, Sloane decided to stored the sequences on-line.
The website is located at http://OEIS.org, and there have been already collected more
than 200,000 sequences. In this thesis, I study an integer sequence which is called
Anti-Fibonacci numbers. The definition is due to Philippe Lalloue (on May 2008) and
on October 2014 Doug Hofstader named it as Anti-Fibonacci number. We establish the
formula for the general term of Anti-Fibonacci numbers. Besides that, we also provide a
programming code for generating Anti-Fibonacci numbers with different initial terms by
MATLAB.

1 Background and Introduction
1.1 Integer Sequence
1.2 Utterly Odd Numbers
1.3 Fibonacci Numbers
1.4 Anti-Fibonacci Numbers Definition By Doug Hofstader

2 Anti-Fibonacci Numbers
2.1 Introduction and Background
2.2 Anti-Fibonacci Numbers of the Second Kind
2.3 Formula via the Utterly Odd Number Method

3 Unique Factorization Method v.s. Utterly Odd Number Method
3.1 Unique Factorization Method
3.2 Utterly Odd Method
3.3 Comparison

4 Utterly Even Numbers
4.1 Introduction
4.2 Utterly Odd Numbers v.s. Utterly Even Numbers
4.3 Application to Anti-Fibonacci Numbers

5 Future Studies

Appendix Anti-Fibonacci Coding and Output

[1] N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences.

[2] Doug Hofstadter, Anti-Fibonacci numbers. Manuscript, 2014.

[3] Anti-Fibonacci Number by Thomas Zaslavsky,Binghamton University (SUNY),
September 26, 2016