minimal perimeter of a polyhex

[Max Alekseyev]

On Wed, Mar 5, 2008 at 9:14 AM, David W. Wilson <wilson.d at anseri.com> wrote:
> As far as I can determine:
>
>  a(0) =
>     0, if n = 0
>     a(n-1) + 2(#{k >= 0: n = [(k^2+15)/12]})
>
>  I initially hoped for a solution of the form
>
>     a(n) = 2[sqrt(12n + something)]
>
>  but a(n) looks a little to bumpy.

The above recurrence indeed implies the following formula:

a(n) = 2*[sqrt(12*n-8)] + 2  for n>=1.

So, your guess is correct.

Regards,
Max




Could some sequence fan with access to JSTOR kindly


MR0929559 (89c:11015) Battiato, S.; Borho, W. Are there odd amicable numbers not divisible by three? Math. Comp. 50 (1988), no. 182, 633--637. (Reviewer: F. T. Howard) 11A51

(so the journal is Mathematics of Computation)

The sequence is in Table 2.  Well, there are really
two sequences, the lower member of each amicable pair
and the upper member.

The numbers are very large, which
is why i don't want to type them!

If you can help, please post a note here

Thanks!

Neil