[seqfan] Re: What are the possible digit-sums for Fibonacci numbers?

Sven Simon sven-h.simon at gmx.de
Fri Jan 6 18:54:04 CET 2017


The factor between Lucas and Fibonacci numbers with same index is about 2.23, just to look up.
Sven

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Von: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] Im Auftrag von Sven Simon
Gesendet: Freitag, 6. Januar 2017 12:59
An: 'Sequence Fanatics Discussion list'
Betreff: [seqfan] Re: What are the possible digit-sums for Fibonacci numbers?

>> It would be nice to settle some of these zeros!

>Not gonna happen. :)

I cannot resist making that remark:
When you take a look at sequence A025490 (Fibonacci numbers with sum of digits in base 11 equals index) and sequence A025491 (same for Lucas numbers) you can see that sometimes things just happen:

A025490 (Fibonacci numbers with 710 elements in complete) ,,,
708   1480167
709   1576621
710   1636597

A025491 (Lucas numbers with 284 elements in complete) ...
281   948539
282   973261
283   983101
284 2528952

Interesting is the fact, that you have much more elements with Fibonacci numbers than with Lucas numbers, in spite the count of digits  of the numbers with same index is almost the same (factor 1,618 on the numbers) and that David Terr in his article (linked with A025490) predicted the count of Fibanacci numbers as 684+-26 - so that matches. There are some internal properties, that make the difference and Terr explains that in his article. A025491 was calculated up to index 7500000 so to be a bit more sure that there are no more remaining numbers. A proof is not possible as far I know.

Sven


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