[seqfan] Conway's subprime Fibonacci sequences
mathoflove-seqfan at yahoo.com
Tue Jul 24 16:26:42 CEST 2012
I just coauthored a paper "Conway's subprime Fibonacci sequences" with Richard K. Guy and Julian Salazar. The paper is in the arxiv: http://arxiv.org/abs/1207.5099
The main sequence (starting with 0,1) should be submitted. In July, I am working at RSI and do not have time to breath. Please, submit.
The rule is: the next term is the sum of the two previous terms, and, if the sum is composite, it is divided by the least prime factor.
Let me illustrate what is going on. First we start with two integers.
Let's take 1 and 1 as in the Fibonacci sequence. Then the next term is
2, because it is prime and we do not divide by anything. The next two
terms are 3 and 5. After that the sum of two terms is 8, which is now
composite and it is divided by 2. So the sequence goes: 1, 1, 2, 3, 5,
4, 3, 7, 5, 6, 11 and so on.
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