Hi, Bram:

Following your posted link, I saw this question on your site:

*"Properties of a number. Does the number 3.35988566622 ring a bell? In connection with Fibonacci?*

You'll get this number adding the reciprocals of the elements of the Fibonacci series (the HP-32SII

program needed 56 of them to yield 11 stable decimals). It's not twice the golden ratio Phi nor have

I found any other relation between Phi and the summed value. [...] From all these ratios and reciprocals I concluded that the sum of reciprocals of the Fib series must

have a relation with Phi, but I'm still searching."

Just in case you're still searching (or interested), you'll find some interesting facts about your constant,

3.359885666243177553172011302918927179688905133655...

at these URLs:

On-Line Encyclopedia of Integer Sequences!

MathWorld

In particular, your constant it's been proved irrational, but doesn't seem to be trivially expressible in terms of other known constants (such as Pi, e, the golden ratio, etc), so either stop searching altogether to save effort, or else persevere and should you find some representation in terms of other known constants you'll make mathematical headlines all over the world.

Menwhile, to help alleviate the frustration and for sheer fun, instead of summing the reciprocals of the Fibonacci numbers, try and find the related sum:

n->Inf

------

1 \ Fib(n)

S = -- * ) ------

10 / 10^n

------

n = 1

where Fib(n) is the n-th Fibonacci number, like this:

Fib(1)=1, Fib(2)=1, Fib(3)=2, Fib(4)=3, Fib(5)=5, etc.

First obtain the value of the sum to a suitable precision, then see if you can recognize what the resulting constant is made of.

Best regards from V.

*Edited: 6 Oct 2004, 12:59 p.m. *