[seqfan] Re: Offsets of Large Integers Decomposed into Decimal Digits
M. F. Hasler
oeis at hasler.fr
Mon Jun 16 13:15:37 CEST 2014
My personal point of view is that integers should have the "fini" kw
and any "decimal expansion" should be c = sum_{i>=offset} a(i) / 10^i
This would put an end to all the confusion and problems due to the
inconsistent "decreasing indices" convention and the fact that all
indices are off by 1 w.r.t. the power of 10 the corresponding digit
represents.
Maximilian
On Mon, Jun 16, 2014 at 1:11 AM, Neil Sloane <njasloane at gmail.com> wrote:
>> For example, the decimal expansion of 3^3^3^3 <https://oeis.org/A241292 >
> is given a huge offset equal to the number of decimal digits in the
> integer. Doesn't it make more sense to see the expansion as a finite *list*
> of digits with offset 1?
>
> OK, as long as you are just talking about large /integers/, that
> seems like a reasonable suggestion.
>
> Neil
>
>
> On Sun, Jun 15, 2014 at 10:53 PM, Hans Havermann <gladhobo at teksavvy.com>
> wrote:
>
>> On Jun 15, 2014, at 8:43 PM, Neil Sloane <njasloane at gmail.com> wrote:
>>
>> > Dear Hans, I understand your point...
>>
>> I'm not sure that you do. All of your examples are non-integers. I don't
>> have a problem with the offsets of those. Integers are constants of a
>> different kind: They can be decomposed in two ways: left-to-right and
>> right-to-left. Suppose someone wanted to contribute the decimal digits of a
>> large number like 9^9^9^9^9. They couldn't do it left-to-right because we
>> can't calculate the first few digits of that expansion. But we can describe
>> this number right-to-left: the units digit, the tens digit, the hundreds
>> digit, etc. Now, think about this sequence. It's not a constant. It doesn't
>> end in a decimal point. It's just a finite list of digits with offset 1.
>> Why should the left-to-right description of a large integer be seen as
>> fundamentally different than the right-to-left description?
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