[seqfan] Re: A083207 On an observation of Frank Buss.

[Donald Alan Morrison]

On Sun, Aug 1, 2010 at 12:57 PM, Donald Alan Morrison
<donmorrison at gmail.com> wrote:
>> If you take the intersection of the zk numbers and the squarefree
>> numbers (in the same region), the intersection's max deltas will all
>> be multiples of 12.  Their intersection contains no primes (since no
>> zk can be prime).  The zk numbers are a special case of the
>> NP-Complete problem (the partition problem).
>
> tdeltas = [(24, 30), (36, 174), (48, 762), (72, 5106)] # tuple (delta, i)
>
> sage: f = map(factor, flatten(tdeltas))
> sage: for a in f:
> ....:     print a
> ....:
> 2^3 * 3
> 2 * 3 * 5
> 2^2 * 3^2
> 2 * 3 * 29
> 2^4 * 3
> 2 * 3 * 127
> 2^3 * 3^2
> 2 * 3 * 23 * 37
>

Also the ratio of the intersection count to the zk count in the
interval is 2380:10000, which is almost 24%...note 24 being a multiple
of 12 as well.

Sorry for the multiple emails.  Email on exponential backoff. ;-)...

Cheers,
Don