[seqfan] Re: Cumulative multiplication

[Alex Meiburg]

When considering the sequence in ternary, we get an interesting
simplification: the sequence is exactly the powers of two without a 0
digit, minus the element 4.' (This is easy to see: 2 is the only factor
that ever enters.) When treating 0s as 1s, it's all powers of 2 except 4.

In quaternary, it's all powers of 3 that contain no 0s or 2s, plus the
element 2.
On Apr 30, 2015 12:43 AM, "Bob Selcoe" <rselcoe at entouchonline.net> wrote:

> Hi Seqfans,
>
> It's interesting how many of the numbers are divisible by prior numbers.
> For example:
>
> 3682784876146817236992 / 28771756844897009664 = 891981549010944
> 28771756844897009664 / 611784327168 = 47029248
> 611784327168 / 4161798144 = 147
> 4161798144 / 4128768 = 1008
> 4128768 / 18432 =224
> 18432 / 384 = 48
> 384 / 128 = 3
>
> and:
>
> 13395375 / 735 = 18225
> 13395375 / 175 = 76545
>
> among others.
>
> Any idea as to why this is?  Might this help giver to clues to (possibly)
> finding larger numbers with this property, if any exist?
>
> Cheers,
> Bob Selcoe
>
> --------------------------------------------------
> From: "Max Alekseyev" <maxale at gmail.com>
> Sent: Wednesday, April 29, 2015 3:42 PM
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: Cumulative multiplication
>
>  There are no other terms below 10^300.
>> The sequence is subsequence of A007602 and likely of A128606 and A257554.
>> The latter (which intersection of the former two) itself is likely finite.
>> Below 10^300 it has 66 terms with the largest containing just 46 digits.
>>
>> Regards,
>> Max
>>
>> On Wed, Apr 29, 2015 at 10:11 AM, M. F. Hasler <oeis at hasler.fr> wrote:
>>
>>  Congratulations! Great work, Giovanni!
>>> It is indeed nice when live surprises us --
>>> provided it is a nice surprise as this one... :D !
>>> This came insofar more as a surprise, as I just had proposed this
>>> sequence as https://oeis.org/draft/A257275 maybe 15 minutes before you
>>> sent your message.
>>>
>>> Wishing a very nice day to all SeqFans,
>>> Maximilian
>>>
>>>
>>> On Wed, Apr 29, 2015 at 10:04 AM, Giovanni Resta <g.resta at iit.cnr.it>
>>> wrote:
>>> > On 04/19/2015 05:15 AM, David Wilson wrote:
>>> >>
>>> >> I would be very surprised if we found any more good numbers.
>>> >
>>> >
>>> > Isn't it nice when life surprises us ?
>>> >
>>> > 3682784876146817236992 = p(3682784876146817236992) * p(3682784876).
>>> >
>>> >
>>> > (No other < 10^100. If we allow to multiply digits from both ends
>>> > of the number, like in
>>> > 4794391461888 = 8*8*8*(4*7*9*4*3*9*1*4*6*1*8*8*8)*4*7, then the
>>> > non trivial such numbers < 10^100 are
>>> > 128, 175, 384, 735, 1296, 18432, 34992, 442368, 4128768, 13395375,
>>> > 13436928, 161243136, 1269789696, 4161798144, 149824733184,
>>> > 611784327168, 4794391461888, 2877833474998272, 3682784876146817236992.)
>>> >
>>> > Giovanni
>>> >
>>> >
>>> >
>>> > _______________________________________________
>>> >
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>>>
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>>>
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>>
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