A066635 Distance from n to closest square different from n.

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

Offset

1,4

Comments

The oscillatory nature of the sequence with increasing amplitude is quite evident.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

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

Example

a(11) = 2 as 11 is closer to 9 than to 16 and 11 - 9 = 2.

Maple

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

Crossrefs

Sequence in context: A222593 A107033 A115110 * A016568 A327314 A021888

Adjacent sequences: A066632 A066633 A066634 * A066636 A066637 A066638

Keyword

easy,nonn,look,changed

Author

Amarnath Murthy, Dec 29 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 03 2002

Status

approved