thank you so much for the help on the (expt A 400) problem... i'm trying to digest / process your comments now.



(2236 squared) ===== 4,999,696
(83666 squared) ===== 6999999556

https://oeis.org/A036516
Smallest square containing exactly n 9's.
9, 3969, 29929, 1999396, 299739969, 2909199969, 19299599929, 909995799969, 9499999990849, .........


i'm wondering if there's something interesting about these numbers.

1.-- How the numbers tend to be ( 1999... 2999... ) is a bit like Benford's law

2. -- In the following, where the 1st column has [0], the square is div. by 9.

Perhaps these (div. by 9) squares in this list will become more rare (as the numbers get bigger)
----- just a hunch/guess

0 - 9
0 - 3969
2 - 29929
1 - 1999396
0 - 299739969
0 - 2909199969
2 - 19299599929
0 - 909995799969
1 - 9499999990849
1 - 999999202999696
0 - 9969959993997969
1 - 90949999999997329
2 - 9199999971969929929
1 - 199999969997999200969
1 - 19997911999199999979409
2 - 295191999919994299999969

295191999919994299999969 --- according to Google, this number shows up in exactly one Web page, and the following numbers don't show up at all ------ which is a bit surprising.

Maybe... even with fast computers, extending list with a few more numbers is pretty difficult.

or maybe it's pretty easy using (e.g.) Mathematica ?

1 - 9599845999999199998999729
1 - 29999999992959999995699281
1 - 199922979699799999999939969

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