[seqfan] Re: Minimal k > n such that (4k+3n)(4n+3k) is square
Charles Greathouse
charles.greathouse at case.edu
Sun Dec 22 04:56:47 CET 2013
I had tested my conjecture to 10^4, but no luck on a proof yet.
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
On Fri, Dec 20, 2013 at 9:57 PM, Hans Havermann <gladhobo at teksavvy.com>wrote:
> For small n, empirically, whenever there exists a solution between 109n/4
> and 393n, there is a corresponding solution (but, what is the
> correspondence?) between n and 109n/4.
>
> 13 {916} {132}
> 24 {2509} {157}
> 26 {1832} {264}
> 33 {1657} {481}
> 37 {4888} {184}
> 39 {2748} {396}
> 48 {5018} {314}
> 52 {3664,8053} {528,213}
> 61 {2616} {1048}
> 65 {4580} {660}
> 66 {3314} {962}
> 69 {12004} {244}
> 72 {7527} {471}
> 73 {6457} {577}
> 74 {9776} {368}
> 78 {5496} {792}
> 88 {5037,16741} {1117,277}
> 91 {6412} {924}
> 96 {10036} {628}
> 97 {3793} {1833}
> 99 {4971} {1443}
> 104 {7328,16106} {1056,426}
> 109 {22264} {312}
>
> On Dec 20, 2013, at 4:29 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
> > If there is no n < k < 109n/4 with (4k+3n)(4n+3k) square, then a(n) =
> 393n.
>
>
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