[seqfan] Re: Project: sequences obtained from Gaussian Integers via Penney's binary method of encoding?

[Андрей Заболотский]

As a follow-up to the story about base i-1 encoding of integers:
looks like I have found a formula for the first differences of A066321 (it is submitted there), thus answering the question asked in A066322. Presumably, all first differences are in A282137. I did not prove it, but doing it seems not very hard.


Regarding an index entry for the sequences related to base i-1 encoding, personally I find this suggestion OK, but generally the practical procedure of introducing and discussing new index entries seems absolutely unclear anyway.

>Суббота, 15 октября 2016, 11:20 +03:00 от Antti Karttunen <antti.karttunen at gmail.com>:
>
>On Sat, Oct 15, 2016 at 6:16 AM,  < seqfan-request at list.seqfan.eu > wrote:
>
>>
>> Message: 26
>> Date: Thu, 13 Oct 2016 00:21:08 +0300
>> From: Андрей Заболотский  < zabolotis at mail.ru >
>> To: Sequence Fanatics Discussion list  < seqfan at list.seqfan.eu >
>> Subject: [seqfan] Re: Project: sequences obtained from Gaussian
>>         Integers via Penney's binary method of encoding?
>> Message-ID: < 1476307268.791062132 at f314.i.mail.ru >
>> Content-Type: text/plain; charset=utf-8
>>
>> Now here is the script for negation and addition of Gaussian integers written in base i-1 with bit twiddling and all that:
>>  http://pastebin.com/uHJW13zf
>> If anyone is interested in its developing, I can put it to Github.
>> It can easily be rewritten in C, but I still used Python to avoid messing with overflows.
>> I used the name "Khmelnik-Penney encoding" not only because Khmelnik's paper was published a bit earlier but also because he did a deep, general analysis of the codes of that kind and the related rules of arithmetics.
>>
>
>So, I suggest that the main Index-entry for this would be located under
>
>https://oeis.org/wiki/Index_to_OEIS:_Section_Ga
>
>as:
>
>Gaussian integers, encoded with Khmelnik-Penney method (base i-1
>expressed as binary vectors, "twindragon base"), sequences related to
>:
>(and this would have an anchor "gaussians_base_twindragon" for
>example. The anchor-part is normally invisible in entries.)
>
>and each entry would then have a link:
>
><a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Ga#gaussians_base_twindragon">Gaussian
>integers, encoded with Khmelnik-Penney method (base i-1)</a>
>
>So it would be very easy to search for them (using the keywords
>"khmelnik", "penney" or "twindragon"), even if not all sequences
>having that link in their Link-section had yet been added under that
>Index-section.
>
>
>And also we should add a forward-link into:
>
>https://oeis.org/wiki/Index_to_OEIS:_Section_Ba
>
>base, i-1 , sequences related to : see Gaussian integers, encoded with
>Khmelnik-Penney method, sequences related to
>
>
>Any suggestions, improvements?
>
>
>
>Best regards,
>
>Antti
>
>--
>Seqfan Mailing list -  http://list.seqfan.eu/



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A066321