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A277425
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a(n) = sqrt(16*t^2 - 32*t + k^2 + 8*k - 8*k*t + 16), where t = ceiling(sqrt(n)) and k = t^2 - n.
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1
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0, 2, 3, 4, 4, 5, 6, 7, 8, 6, 7, 8, 9, 10, 11, 12, 8, 9, 10, 11, 12, 13, 14, 15, 16, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28
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OFFSET
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1,2
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COMMENTS
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The equation 16*t^2 - 32*t + k^2 + 8*k - 8*k*t + 16 always produces a square, for any number n, with any t and k (i.e., t can be incremented and a corresponding k value is produced).
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LINKS
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FORMULA
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EXAMPLE
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n = 3, f(n) = 3; n = 11, f(n) = 7; n = 64, f(n) = 28; n = 103, f(n) = 22; n=208, f(n)= 39.
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MAPLE
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MATHEMATICA
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Table[Function[t, Function[k, Sqrt[16 t^2 - 32 t + k^2 + 8 k - 8 k t + 16]][t^2 - n]]@ Ceiling@ Sqrt@ n, {n, 64}] (* or *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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