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Rosetta: Sequence of non-squares

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> Show that the following remarkable formula gives the sequence
> of non-square natural numbers:
> 
>  n + floor(1/2 + sqrt(n))
> 
> Print out the values for n in the range 1 to 22.
> 
> Show that no squares occur for n less than one million


nsq = Enumerator.new{|y|
  n = 0
  loop {n += 1 ; y.yield(n + Math.sqrt(n).round)}
}

nsq.take 22

 ===>
[2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23,
 24, 26, 27]


def square? n
  m = Math.sqrt(n)
  m.floor == m
end

nsq.lazy.take(999_999).none?{|n| square? n}

 ===>
true

In Forth?


-- 
[E]verything that happens in the world is for the benefit of the Jewish
People....  G-D ... created the world for the sake of the Jewish People, and it
is our responsibility to implement the Torah---absolute morality and the
blueprint of creation---in it.
www.IsraelNationalNews.com/Articles/Article.aspx/2125#.UUnBZxx4xn8

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Rosetta: Sequence of non-squares "Robert L." <No_spamming@noWhere_7073.org> - 2017-05-01 18:24 +0000

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