Sequence of non-squares: Difference between revisions
→{{header|Python}}: Added a definition of A000037 as a non-finite series.
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(→{{header|Python}}: Added a definition of A000037 as a non-finite series.) |
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StopIteration: </lang>
Or, defining OEIS A000037 as a non-finite series:
{{Works with|Python|3.7}}
<lang python>'''Sequence of non-squares'''
from itertools import count, islice
from math import floor, sqrt
# A000037 :: [Int]
def A000037():
'''A non-finite series of integers.'''
return map(nonSquare, count(1))
# nonSquare :: Int -> Int
def nonSquare(n):
'''Nth term in the OEIS A000037 series.'''
return n + floor(1 / 2 + sqrt(n))
# --------------------------TEST---------------------------
# main :: IO ()
def main():
'''OEIS A000037'''
def first22():
'''First 22 terms'''
return take(22)(A000037())
def squareInFirstMillion():
'''True if any of the first 10^6 terms are perfect squares'''
return any(map(
isPerfectSquare,
take(10 ** 6)(A000037())
))
print(
fTable(main.__doc__)(
lambda f: '\n' + f.__doc__
)(lambda x: ' ' + repr(x))(
lambda f: f()
)([first22, squareInFirstMillion])
)
# -------------------------DISPLAY-------------------------
# fTable :: String -> (a -> String) ->
# (b -> String) -> (a -> b) -> [a] -> String
def fTable(s):
'''Heading -> x display function -> fx display function ->
f -> xs -> tabular string.
'''
def go(xShow, fxShow, f, xs):
ys = [xShow(x) for x in xs]
return s + '\n' + '\n'.join(map(
lambda x, y: y + ':\n' + fxShow(f(x)),
xs, ys
))
return lambda xShow: lambda fxShow: lambda f: lambda xs: go(
xShow, fxShow, f, xs
)
# -------------------------GENERAL-------------------------
# isPerfectSquare :: Int -> Bool
def isPerfectSquare(n):
'''True if n is a perfect square.'''
return sqrt(n).is_integer()
# take :: Int -> [a] -> [a]
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.
'''
return lambda xs: list(islice(xs, n))
# MAIN ---
if __name__ == '__main__':
main()</lang>
{{Out}}
<pre>OEIS A000037
First 22 terms:
[2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27]
True if any of the first 10^6 terms are perfect squares:
False</pre>
=={{header|R}}==
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