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A243256
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Smallest distance of the n-th Fibonacci number to the set of all square integers.
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0
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0, 0, 0, 1, 1, 1, 1, 3, 4, 2, 6, 8, 0, 8, 16, 15, 26, 3, 17, 44, 41, 79, 22, 96, 143, 51, 289, 169, 285, 140, 296, 669, 267, 1449, 343, 1979, 144, 592, 665, 4223, 699, 5283, 2872, 19604, 6477, 21826, 17999, 16008, 46080, 31240, 102696, 8638, 45526, 95764
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OFFSET
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0,8
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COMMENTS
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a(n) = 0 if and only if n = 0, 1, 2, 12.
The sorted unique members: 0, 1, 2, 3, 4, 6, 8, 15, 16, 17, 22, 26 ...
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LINKS
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FORMULA
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PROG
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(Sage)
def a(n):
f = fibonacci(n)
return min((floor(sqrt(f))+1)^2 - f, f - floor(sqrt(f))^2)
(PARI) {a(n) = my(f, i); if( n<0, 0, i = sqrtint( f = fibonacci(n))); min(f - i^2, (i+1)^2 - f)}; /* Michael Somos, Jun 02 2014 */
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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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