[seqfan] Re: More (composite) terms for A233281

David Wilson davidwwilson at comcast.net
Sat Feb 15 05:15:48 CET 2014


Just in the name of precision,

The smallest possible prime factor of Fib(p) for prime p is 2p-1 with
exceptions Fib(3) = 2 and Fib(5) = 5.

> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Hans
> Havermann
> Sent: Thursday, February 13, 2014 3:11 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: More (composite) terms for A233281
> 
> "The smallest prime factor of Fib(p) being ~ 2p suggests that the smallest
> composite divisor of Fib(p) exceeds ~ 4*p^2."
> 
> Correction: The smallest possible prime factor of Fib(p) is 2*p-1, the
second-
> smallest possible prime factor is 4*p+1; therefore the smallest possible
> composite divisor of Fib(p) is 8*p^2-2*p-1. For example, (p=37) 73*149,
> (p=97) 193*389, etc. This makes it possible to get all of Antti's
composites <
> 10^11 by looking at Fibonacci factorizations up to (and including)
Fib(111799).
> Doing so yields 338 (barring errors) composites. I've got the second non-
> semiprime (1453*2909*10177) as #254.
> 
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