# [seqfan] Re: A175287: n = 3^k3 + 5^k5 + 7^k7

Charles Greathouse charles.greathouse at case.edu
Mon Mar 22 15:14:07 CET 2010

```Has a Størmer's theorem-type result on the finitude of this kind of
sequence been proven?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Mon, Mar 22, 2010 at 6:59 AM, zak seidov <zakseidov at yahoo.com> wrote:
> Open to discussion (not submitted yet),
> thanks,
> Zak
>
> %I A175287
> %S A175287 135,255,375,2535,3135,3155,3255
> %N A175287 Numbers n with two representations as the sum of positive powers of 3,5 and 7.
> %C A175287 Except of 3155 all terms are divisible by 15.
> %C A175287 No other terms <7^180 (<132*10^150).
> %C A175287 Values of {k3,k5,k7}:
> %C A175287 n=135, {1,3,1},{4,1,2}
> %C A175287 n=255, {4,3,2},{5,1,1}
> %C A175287 n=375, {3,1,3},{5,3,1}
> %C A175287 n=2535, {2,3,4},{7,1,3}
> %C A175287 n=3135, {1,5,1},{6,1,4}
> %C A175287 n=3155, {6,2,4},{7,4,3}
> %C A175287 n=3255, {4,5,2},{6,3,4}.
> %F A175287
> %Y A175287 135=3+25+7=81+5+49, 255=81+125+49=243+5+7, 375=27+5+343=243+125+7.
> %K A175287 nonn
> %O A175287 1,1
> %A A175287 Zak Seidov (zakseidov(AT)yahoo.com), Mar 22 2010
>
>
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

```