As for Q1:
No luck in searching for something like 3.3598856662 .
What finally produced some relavant entries was
(a) using search words 'fibonacci' and 'reciprocal', or
(b) writing the number explicitely as "3 3 5 9 8 8 5 6 6 6 2" oeis .
This led me to e.g. OEIS A079586 (https://oeis.org/A079586) .
Means that the series *converges* to what Eric Weisstein calls the
'Reciprocal Fibonacci Constant'
(https://mathworld.wolfram.com/ReciprocalFibonacciConstant.html) .
As for Q2:
No result so far; will report back.
Thanks.
-M
At 2022-12-26 18:39, you wrote:
I don't know about naming here, but if you are going to attempt
searching on numeric results, you might want something more precise
than ^^. to obtain a decimal representation.
For example:
0j16 ": 851897554247r254074700880
3.3529412857573449
I hope this helps,
--
Raul
On Mon, Dec 26, 2022 at 6:50 AM Martin Kreuzer <[email protected]> wrote:
> Hi all --
> - 1 -----
> Inspired by lately reading up on the Kempner series I tried this
> modification (depletion) of the harmonic series:
> fib >: i.13
> 1 1 2 3 5 8 13 21 34 55 89 144 233
> % fib >: i.13
> 1 1 1r2 1r3 1r5 1r8 1r13 1r21 1r34 1r55 1r89 1r144 1r233
> +/ % fib >: i.13
> 851897554247r254074700880
> ^^. +/ % fib >: i.13
> 3.35294128575735
> NB. ...
> ^^. +/ % fib >: i.50
> 3.3598856661144394
> ^^. +/ % fib >: i.60
> 3.3598856662422096
> ^^. +/ % fib >: i.70
> 3.3598856662429739
> ^^. +/ % fib >: i.80
> 3.3598856662433558
> and have been wondering about convergence/divergence.
> - 2 -----
> In parallel I did this
> fib i.13
> 0 1 1 2 3 5 8 13 21 34 55 89 144
> ecf fib i.13
> 2882971364492r4895735924493
> ^^. ecf fib i.13
> 0.588874
> NB. (fib) producing Fibonacci numbers
> NB. (ecf) evaluating a Continued Fraction
> and have wondered whether this constant had a name (since the Fib
> numbers themselves are fairly famous), and in what other contexts it
> might pop up.
> NB. The Wolfram|Alpha equivalent would have been
> NB. FromContinuedFraction[Fibonacci[Range[0,13]]]
> -----
> Could you shed some light on these (while keeeping in mind that I'm
> not a mathematician).
> Thanks (and with season's greetings)
> -M
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