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A276689
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Least term in the periodic part of the continued fraction expansion of sqrt(n) or 0 if n is square.
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2
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0, 0, 2, 1, 0, 4, 2, 1, 1, 0, 6, 3, 2, 1, 1, 1, 0, 8, 4, 1, 2, 1, 1, 1, 1, 0, 10, 5, 2, 1, 2, 1, 1, 1, 1, 1, 0, 12, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 0, 14, 7, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 16, 8, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 18, 9, 6, 1
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OFFSET
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0,3
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COMMENTS
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If r > 0 is even, then a((rm/2)^2+m) = r for all m >= 1 and a((r^2-2)^2/4 + (r+1)^3) = r.
If r is odd, then a((rm)^2+2m) = r for all m >= 1 and a(r^4 + r^3 + 5(r+1)^2/4) = r.
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LINKS
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PROG
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(Python)
from sympy import continued_fraction_periodic
x = continued_fraction_periodic(0, 1, n)
return min(x[1]) if len(x) > 1 else 0
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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