[seqfan] Re: Sirag numbers.

Charles Greathouse charles.greathouse at case.edu
Fri Sep 30 05:59:50 CEST 2011


> Sirag numbers are 2-automatic, that is, there is a finite automaton that
> accepts precisely their base-2 numerals.

Where does that term come from?  I've used "2-regular" in the same way
(cf. A038772).

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Thu, Sep 29, 2011 at 11:38 PM, David Wilson <davidwwilson at comcast.net> wrote:
> On 9/29/2011 2:32 PM, franktaw at netscape.net wrote:
>>
>> From basic number theory, n is a Sirag number iff n*(n+1) = 4^j * (8k+7)
>> for some integer j and k.
>>
>> Franklin T. Adams-Watters
>
> Ergo, Sirag numbers n are characterizable as one of the following forms:
>
> n == 12 (mod 32)
> n == 19 (mod 32)
> n = 4^j*(8k+1)-1 (j >= 2; k >= 0)
> n = 4^j*(8k+7)  (j >= 2; k >= 0)
>
> and can be shown to have limit density 1/12 with respect to the integers.
>
> Sirag numbers are 2-automatic, that is, there is a finite automaton that
> accepts precisely their base-2 numerals.
>
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