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A249142
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Let k be the difference between the smallest square >= n and n. Sequence gives difference between the smallest square >= k and k.
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2
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0, 2, 0, 0, 0, 1, 2, 0, 0, 3, 4, 0, 1, 2, 0, 0, 1, 2, 3, 4, 0, 1, 2, 0, 0, 6, 0, 1, 2, 3, 4, 0, 1, 2, 0, 0, 4, 5, 6, 0, 1, 2, 3, 4, 0, 1, 2, 0, 0, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 0, 1, 2, 0, 0, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 0, 1, 2, 0, 0, 7, 8, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 0, 1, 2, 0, 0
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = n - ceiling(sqrt(n))^2 + ceiling(sqrt(-n+ceiling(sqrt(n))^2))^2.
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EXAMPLE
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For n = 13 the next biggest square is 16, thus k = 16 - 13 = 3 and for 3 the next biggest square is 4, thus a(14) = 3 - 2 = 1.
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MAPLE
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A068527:= n -> ceil(sqrt(n))^2 - n:
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MATHEMATICA
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Table[n - Ceiling[Sqrt[n]]^2 + Ceiling[Sqrt[-n + Ceiling[Sqrt[n]]^2]]^2, {n, 1, 100}]
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PROG
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(PARI) A068527(n)=if(issquare(n), 0, (sqrtint(n)+1)^2-n)
(Magma) [n - Ceiling(Sqrt(n))^2 + Ceiling(Sqrt(-n+Ceiling(Sqrt(n))^2))^2: n in [1..100]]; // Vincenzo Librandi, Oct 23 20124
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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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EXTENSIONS
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Edited, old crossrefs entry moved to Comments, and first two formula lines interchanged by Wolfdieter Lang, Nov 10 2014
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STATUS
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approved
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