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A260374
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The distance between n! and the nearest perfect square.
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2
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0, 0, 1, 2, 1, 1, 9, 1, 81, 476, 225, 324, 4604, 74879, 176400, 215296, 3444736, 11551671, 45680444, 255004929, 1158920361, 2657058876, 24923993276, 130518272975, 97216010329, 2430400258225, 1553580508516, 4666092737476, 538347188396016, 2137864362693921
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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LINKS
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Table of n, a(n) for n=0..29.
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FORMULA
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a(n) = abs(n!-A260373(n)).
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EXAMPLE
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6!=720. The nearest perfect square is 729. The difference between these is 9, so a(6)=9.
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PROG
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(PARI) a(n)=abs(n!-round(sqrt(n!))^2) \\ Charles R Greathouse IV, Jul 23 2015
(Python)
from gmpy2 import isqrt
A260374_list, g = [0], 1
for i in range(1, 1001):
....g *= i
....s = isqrt(g)
....t = g-s**2
....A260374_list.append(int(t if t-s <= 0 else 2*s+1-t)) # Chai Wah Wu, Jul 23 2015
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CROSSREFS
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Cf. A260373, A260375.
Sequence in context: A087127 A144946 A332717 * A157109 A185814 A174553
Adjacent sequences: A260371 A260372 A260373 * A260375 A260376 A260377
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KEYWORD
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nonn
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AUTHOR
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Otis Tweneboah, Pratik Koirala, Eugene Fiorini, Nathan Fox, Jul 23 2015
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STATUS
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approved
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