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

Max Alekseyev maxale at gmail.com
Sat Nov 15 20:16:08 CET 2014


Ops, I've caught the bug and it turns out that there are terms before
(10^111-1)/9.
Namely,
(10^106-1)/9 + 122222222
and all its permutations.

Regards,
Max


On Sat, Nov 15, 2014 at 12:53 PM, Max Alekseyev <maxale at gmail.com> wrote:
> 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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