# [seqfan] Re: binary expansion 1+0*

Paul D Hanna pauldhanna at juno.com
Mon Mar 22 21:00:05 CET 2010

SeqFans,
It is curious to note that:

Product_{n>=1} 1/(1 - x^A023758(n)) = g.f. of A087750 (when including A087750(0)=1).

where A087750(n) is the number of partitions of n into numbers having in binary representation at most trailing zeros.

It does not appear that the sequence having g.f.:
Product_{n>=1} (1 - x^A023758(n))
is in the OEIS.

Paul

* franktaw at netscape.net <franktaw at netscape.net> [Mar 22. 2010 19:01]:
> You seem to be missing some numbers: the powers of 2 (other than 1,
> which you have).  When you put them in, the sequence is A023758.
>
>
> -----Original Message-----
> From: Joerg Arndt <arndt at jjj.de>
>
> starts as
> 1, 3, 6, 7, 12, 14, 15, 24, 28, 30, 31, 48, 56, 60, 62, 63, 96, 112,
> 120, 124,
> 126, 127,
>
> Numbers of the form (2^k-1)*2^j for k>=1 and j>=0
>
> Interesting(?) property:
> For all a(n)>1 the set (2^j)%a(n)
> consists only of the powers of two.
>
>
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