General Fibonacci Sequence whose Terms are all Composite
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Theorem
The general Fibonacci sequence $\left\langle{a_n}\right\rangle$ defined as:
- $a_n = \begin{cases} r & : n = 0 \\ s & : n = 1 \\ a_{n - 2} + a_{n - 1} & : n > 1 \end{cases}$
where:
- $r = 62 \, 638 \, 280 \, 004 \, 239 \, 857$
- $s = 49 \, 463 \, 435 \, 743 \, 205 \, 655$
is such that:
Proof
This theorem requires a proof. In particular: Knuth proves it in the citation given. Needs to be transcribed, but it's boring and I can't be bothered. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Sources
- Feb. 1990: Donald E. Knuth: A Fibonacci-Like Sequence of Composite Numbers (Math. Mag. Vol. 63, no. 1: pp. 21 – 25) www.jstor.org/stable/2691504
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $62,638,280,004,239,857$