a(n) = Smallest Multiple Of a(n-1) With Exactly n Binary 1's

[Max Alekseyev]

On Mon, Jul 21, 2008 at 1:29 PM, Jack Brennen <jb at brennen.net> wrote:
> Leroy Quet wrote:
>>
>> Let a(1) = 1. Let a(n) = the smallest positive multiple of a(n-1) with
>> exactly n 1's in its binary representation.
>>
>> The sequence begins (though, I could be wrong, of course): 1,3,21,105,...
>>
>
> It continues ...,4305,21525,5316675,3291021825,...
>
>
> The next term is > 2^59, but less than or equal to
>   295167045907433652225.

The next term is: 38046409656325181475

so that the sequence starts with

1, 3, 21, 105, 4305, 21525, 5316675, 3291021825, 38046409656325181475,

According to my computations, the next term is longer than 110 bits.
Heuristic arguments suggest that its binary length is above 400.

Regards,
Max