RetroBBS - comp.lang.scheme - Squares with N 9's = 9, 3969, 29929, 1999396, ... -- (extending the List ?)

Squares with N 9's = 9, 3969, 29929, 1999396, ... -- (extending the List ?)

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Subject: Squares with N 9's = 9, 3969, 29929, 1999396, ... -- (extending the
List ?)
From: henhanna@gmail.com (Hen Hanna)
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by: Hen Hanna - Sat, 18 Jun 2022 22:56 UTC

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

Subject	Author
Squares with N 9's = 9, 3969, 29929, 1999396, ... -- (extending the	Hen Hanna

There's a whole WORLD in a mud puddle! -- Doug Clifford

devel / comp.lang.scheme / Squares with N 9's = 9, 3969, 29929, 1999396, ... -- (extending the List ?)