# [seqfan] Re: Rule needed

David Wilson dwilson at gambitcomm.com
Mon Nov 10 19:26:42 CET 2008

```So you're working on the old ABC conjecture, eh?

I doubt you're going to find the magic formula you are looking for, all
the mysteries of number theory are wrapped up in it. But good luck and
keep us posted.

Artur wrote:
> Dear Seqfans,
> I need help with finding rule on follwing problem
> Sequences:
> B={1, 3, 7, 15, 27, 63, 125, 243, 343, 999, 1805, 3721, 8181, 16335,
> 32761, 65533, 112847, 190269, 519375, 1046875, 1953125}
> C={2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384,
> 32768, 65536, 131072, 262144, 524288, 1048576, 2097152}
> A={1, 1, 1, 1, 5, 1, 3, 13, 169, 25, 243, 375, 11, 49, 7, 3, 18225,
> 71875, 4913, 1701, 144027}
> C(n) = 2^n
> A(n) = C(n) - B(n)
> A(n) < B(n) < C(n)
> is obtained by algorhitm such
> that GCD[A(n),B(n),C(n)] = 1 and product of distinct prime divisors of
> A(n)*B(n)*C(n) have minimal value.
> I'm looking for formula for B(n).
> Who can help?
> Best wishes
> Artur
>

```