A249142 Let k be the difference between the smallest square >= n and n. Sequence gives difference between the smallest square >= k and k.

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

Offset: 1

Author

Valtteri Raiko, Oct 22 2014

Keywords

• nonn
• easy

Comments

Equals A068527 applied to itself.

Examples

			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.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A068527.

Programs

Magma

[n - Ceiling(Sqrt(n))^2 + Ceiling(Sqrt(-n+Ceiling(Sqrt(n))^2))^2: n in [1..100]]; // Vincenzo Librandi, Oct 23 2014

Maple

A068527:= n -> ceil(sqrt(n))^2 - n:
map(A068527@@2, [$1..100]); # Robert Israel, Nov 02 2017

Mathematica

Table[n - Ceiling[Sqrt[n]]^2 + Ceiling[Sqrt[-n + Ceiling[Sqrt[n]]^2]]^2, {n, 1, 100}]

PARI

A068527(n)=if(issquare(n), 0, (sqrtint(n)+1)^2-n)
a(n)=A068527(A068527(n)) \\ Charles R Greathouse IV, Oct 22 2014

Formula

a(n) = A068527(A068527(n)).

a(n) = n - ceiling(sqrt(n))^2 + ceiling(sqrt(-n+ceiling(sqrt(n))^2))^2.

a(n) < (64n)^(1/4). - Charles R Greathouse IV, Oct 22 2014

Extensions

Edited, old crossrefs entry moved to Comments, and first two formula lines interchanged by Wolfdieter Lang, Nov 10 2014