squarewise concatanation for the win

[fatphil]

1225172265625 is a lovely number
1 is a square
225 is a square
put them together, and 1225 is a square
72265625 is a square
put it together with what came before, and you get
122572265625 which is a square

I don't know where I'm going with this, but I'm sure you guys can have fun.
(oh, 4 and 9 have even shorter paths, but ones I've not probed as deeply)

[Dr Sardonicus]

Originally Posted by fatphil

1225172265625 is a lovely number
1 is a square
225 is a square
put them together, and 1225 is a square

So far, so good.

72265625 is a square

Er, no.

? print(factor(72265625))
[5, 9; 37, 1]

put it together with what came before, and you get
122572265625 which is a square
<snip>

Again, no.

? print(factor(122572265625))
[3, 2; 5, 9; 19, 1; 367, 1]

[fatphil]

Originally Posted by Dr Sardonicus

So far, so good.
Er, no.

? print(factor(72265625))
[5, 9; 37, 1]

Again, no.

? print(factor(122572265625))
[3, 2; 5, 9; 19, 1; 367, 1]

Ooops, missed a character in the copy/paste:
? factor(172265625)

[3 2]
[5 8]
[7 2]

? factor(1225172265625)

[ 5 8]
[ 7 2]
[11 2]
[23 2]

[fatphil]

Originally Posted by fatphil

1225172265625 is a lovely number
I don't know where I'm going with this, but I'm sure you guys can have fun.
(oh, 4 and 9 have even shorter paths, but ones I've not probed as deeply)

It appears that probing's quite cheap:

4 -> 49 -> 49729 -> 4972922562328439750054749703581033600295913998934338451363146305084228515625

9 -> 950625 -> 95062561096409435940120435784167300872787977524634772310552222052137949503958225250244140625