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A066635
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Distance from n to closest square different from n.
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6
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1, 1, 1, 3, 1, 2, 2, 1, 5, 1, 2, 3, 3, 2, 1, 7, 1, 2, 3, 4, 4, 3, 2, 1, 9, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 11, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 13, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 15, 1, 2, 3, 4, 5, 6, 7, 8, 8, 7, 6, 5, 4, 3, 2, 1, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 1, 2
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OFFSET
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1,4
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COMMENTS
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The oscillatory nature of the sequence with increasing amplitude is quite evident.
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LINKS
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FORMULA
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a(n) = Min {n - floor(sqrt(n))^2, (floor(sqrt(n))+1)^2 - n} if n is not a square. a(n) = 2*sqrt(n) - 1 if n is a square.
G.f. -x^2/(1-x)^2 + Sum_{m>=1} x^(m^2)*(2m - x^m*(x+x^2)/(1-x)^2 -(1-4*x+x^2)/(1-x)^2). - Robert Israel, Nov 07 2017
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EXAMPLE
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a(11) = 2 as 11 is closer to 9 than to 16 and 11 - 9 = 2.
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MAPLE
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N:= 10: # to get a(1)..a((N+1)^2-1)
seq(op([m^2-(m-1)^2, seq(i-m^2, i=m^2+1..m^2+m), seq((m+1)^2-i, i=m^2+m+1..(m+1)^2-1)]), m=1..N); # Robert Israel, Nov 07 2017
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Apr 03 2002
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STATUS
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approved
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