[seqfan] Re: Sirag numbers.

[David Wilson]

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.