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 2023-03-18, 21:22 #1 fatphil     May 2003 4028 Posts squarewise concatanation for the win 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)
2023-03-19, 13:12   #2
Dr Sardonicus

Feb 2017
Nowhere

22·3·17·31 Posts

Quote:
 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.
Quote:
 72265625 is a square
Er, no.
Code:
? print(factor(72265625))
[5, 9; 37, 1]
Quote:
 put it together with what came before, and you get 122572265625 which is a square
Again, no.
Code:
? print(factor(122572265625))
[3, 2; 5, 9; 19, 1; 367, 1]

2023-03-19, 13:54   #3
fatphil

May 2003

2·3·43 Posts

Quote:
 Originally Posted by Dr Sardonicus So far, so good. Er, no. Code: ? print(factor(72265625)) [5, 9; 37, 1] Again, no. Code: ? 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]

2023-03-19, 14:21   #4
fatphil

May 2003

1000000102 Posts

Quote:
 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

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