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

[Max Alekseyev]

I'd like to point out that a related problem of finding Fibonacci numbers
with a given digitsum is hard even in base 2 -- see https://oeis.org/A222296
Noam Elkies proved that digitsum=2 is delivered only by Fibonacci
numbers 3, 5, 34, 144.
However, already for digitsum=3, it is an open question to determine if
there are any other Fibonacci numbers besides 13 and 21.

Regards,
Max

On Mon, Dec 26, 2016 at 4:17 PM, Neil Sloane <njasloane at gmail.com> wrote:

> A067182:
>
> Smallest Fibonacci number with digit sum n, or 0 if no such number exists:
> 0, 1, 2, 3, 13, 5, 0, 34, 8, 144, 55, 0, 0, 0, 4181, 0, 0, 89, 0, 2584,
> 10946, 317811, 1597, 514229, 987, 0, 0, 46368, 28657, 196418, 2178309,
> 1346269, 0, 701408733, 3524578, 9227465, 0, 5702887, 0, 0, 0, 433494437, 0,
> 63245986, 39088169, 0, 267914296, 0
>
> COMMENTS
>
> The zeros are just conjectures.
> --------
>
> It would be nice to settle some of these zeros!
>
> I don't know why Gmail is restricting my lines to 15 characters
>
> Neil
>
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