[seqfan] Re: Nominations for A250000 / help needed with A249517.

Max Alekseyev maxale at gmail.com
Sat Nov 15 18:53:21 CET 2014


Hi Neil,

While A249517(11) = 11111111111 was confirmed by Sean A. Irvine, I
confirm that A249517(12) = (10^111-1)/9 (i.e. the repunit with 111
digits).
The next one is likely to be the repunit with 1111 digits and its
verification is in progress.
However, later this pattern breaks. For example, A249517 contains the
following number as well as all permutations of its digits:

(10^1210 - 1)/9 + 1113333888

that is, all numbers composed of 1200 digits 1, three digits 2, four
digits 4, and three digits 9 (with the digit sum 1249).
There are also other numbers that are not repunits. In fact, the
possible digit sums of terms of A249517 form the sequence:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 111, 1111, 1239, 1249, 1267, 1276, ...

Regards,
Max


On Thu, Nov 13, 2014 at 12:40 AM, Neil Sloane <njasloane at gmail.com> wrote:
> Dear Seq Fans, A250000 has been reserved for
> the best sequence submitted in recent months.
> We would like to get some suggestions - send them to me - we have
> deliberately left the rules somewhat vague...
>
> Secondly, Jaroslav Krizek has submitted an interesting sequence, A249517:
> Numbers n for which the digital sum A007953(n) and the digital product
> A007954(n) both contain the same distinct digits as the number n.
>
> The known terms are 0 1 2 3 4 5 6 7 8 9 and
> it is conjectured that the next term is
> 11111111111 - this is not so big - could someone check if it really is the
> next term? Until then the sequence can't really be accepted because it
> overlaps with too many other sequences.
>
> Thanks!
>
> Neil
>
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