6
$\begingroup$

I want to be certain I have the latest information on Conway's subprime Fibonacci sequences, arXiv-posted a year ago; I am referencing the status in a review. To wit, starting with $(0,1)$:1 $$ 0, 1, 1, 2, 3, 5, 4, 3, 7, 5, 6, 11, 17, 14, 31, 15, 23, 19, \ldots $$

Richard K. Guy, Tanya Khovanova, Julian Salazar:
"however, it seems more likely here than in the $3x + 1$ problem that sequences do not increase indefinitely. Here is an informal argument that supports such a conjecture,"

$\color{Red}{Q}$: Has it been established that some sequence increases indefinitely? Or no sequence, regardless of starting conditions, does not?


1"Start with the Fibonacci sequence 0, 1, 1, 2, 3, 5, . . . , but before you write down a composite term, divide it by its least prime factor so that this next term is not 8, but rather 8/2 = 4."

$\endgroup$
  • 3
    $\begingroup$ Also published as Conway’s Subprime Fibonacci Sequences, Richard K. Guy, Tanya Khovanova and Julian Salazar, Mathematics Magazine Vol. 87, No. 5 (December 2014), pp. 323-337. $\endgroup$ – Gerry Myerson Aug 7 '15 at 23:06
4
$\begingroup$

A somewhat different (but related) sequence has been analyzed satisfactorily. Quite recently, too (A Note on Prime Fibonacci Sequences, Jeremy Alm, Taylor Herald (Submitted on 17 Jul 2015)).

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.