[seqfan] Re: Cumulative multiplication

[Bob Selcoe]

Hi Alex  & Seqfans,

Alex - not quite sure I follow:

>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.

Could you please provide a couple of examples of what you mean?

Everyone - I made an error in the previous posting (hazards of manual 
calculations late at night).  It should have read:

3682784876146817236992 / 4794391461888 =  768144384
4794391461888 / 149824733184 = 32
149824733184 / 4161798144 = 36
4161798144 / 4128768 = 1008
4128768 / 18432 =224
18432 / 384 = 48
384 / 128 = 3

Best,
Bob




--------------------------------------------------
From: "Alex Meiburg" <timeroot.alex at gmail.com>
Sent: Thursday, April 30, 2015 4:45 AM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Cumulative multiplication

> 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 = 611784327168
2877833474998272
>> 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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