known (coincidental ?) artifact ?

[franktaw at netscape.net]

It's pretty much obvious.

First of all, simple arithmetic lets us simplify the expression to

a(n) = floor(n^2/10) - floor((n-1)^2/10) + 2

The "+ 2" obviously doesn't affect the pattern of differences,
so what we are really looking at is the pattern of differences in
floor(n^2)/10.   Since the final digit of n^2 depends only
on n modulo 10, and the difference in the squares is 2n-1, this
will have a pattern of changes depending only on the final
digit.

Franklin T. Adams-Watters

-----Original Message-----
From: Alexander Povolotsky <apovolot at gmail.com>

...

 Consider calculating (in decimal system):

floor(n*n/10) + 10

and then looking between the  difference of calculated above and 
"doubled" value of n :

(floor(n*n/10) + 10)  - 2*n

and then look at the differences between in above expression for two 
consecutive integers n and (n-1)

a(n) = ((floor(an*n/10) + 10) - 2*n) - ((floor((n-1)*(n-1)/10) + 10 - 
2*(n-1))

...

So you could notice that starting from a(4) and on - the difference is 
kept the same for first 4 terms and then the difference gets  
incremented by 1 and as such is kept constant for next 6 terms, then it 
increments by 1 again and is kept the same for 4 terms, etc, etc ....

...

Is this well known and/or obvious ?

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