Problem

[Giovanni Resta]

Roberto Tauraso wrote:

> If anybody is interested here are the minimal loops that I found:
>
>http://www.mat.uniroma2.it/~tauraso/Loops/2-loop32.txt
>http://www.mat.uniroma2.it/~tauraso/Loops/3-loop473.txt
>http://www.mat.uniroma2.it/~tauraso/Loops/4-loop9641.txt
>It is interesting to note that the minimal squareloop is unique.
>On the other hand the minimal cubeloop is not unique.
>

Hi,
just curious about the easier chain (not loop) values.
For  squares it is 15 (A107929).
For  cubes I did find 305, i.e., 256, 87, 129, 214, ...,  264, 248, 95
(as reported in the same Rivera's page you cited earlier).
If this value is correct we have the beginning of a sequence: 2, 15, 305,...
Do you know which is the value for 4th powers? I expect it is
smaller than the loop value (9641).

Just for fun: I have recently uploaded the nontrivial-palindromes loop,
of size 66  ( A113819 ) and, b.t.w., the triangular numbers loop seems 
to have length 12:
1, 5, 10, 11, 4, 6, 9, 12, 3, 7, 8, 2.

bye,
g.