[seqfan] Re: Minimal k > n such that (4k+3n)(4n+3k) is square

[Hans Havermann]

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.