Sequence of non-squares
You are encouraged to solve this task according to the task description, using any language you may know.
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
Python
<python> >>> from math import sqrt,floor >>> def nonsqr(n): return n + floor(0.5 + sqrt(n))
>>> # first 22 values (as a list) has no squares: >>> [nonsqr(i) for i in xrange(1,23)] [2.0, 3.0, 5.0, 6.0, 7.0, 8.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 26.0, 27.0] >>> # The following check shows no squares up to one million: >>> for i in xrange(1,1000000): j = sqrt(nonsqr(i)) assert j != int(j), "Found a square in the sequence: %i" % i
>>>
</python>