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A249142
Let k be the difference between the smallest square >= n and n. Sequence gives difference between the smallest square >= k and k.
2
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
1,2
COMMENTS
Equals A068527 applied to itself.
LINKS
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
EXAMPLE
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.
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}]
PROG
(PARI) A068527(n)=if(issquare(n), 0, (sqrtint(n)+1)^2-n)
a(n)=A068527(A068527(n)) \\ Charles R Greathouse IV, Oct 22 2014
(Magma) [n - Ceiling(Sqrt(n))^2 + Ceiling(Sqrt(-n+Ceiling(Sqrt(n))^2))^2: n in [1..100]]; // Vincenzo Librandi, Oct 23 20124
CROSSREFS
Cf. A068527.
Sequence in context: A281542 A331844 A191410 * A225099 A174806 A089605
KEYWORD
nonn,easy
AUTHOR
Valtteri Raiko, Oct 22 2014
EXTENSIONS
Edited, old crossrefs entry moved to Comments, and first two formula lines interchanged by Wolfdieter Lang, Nov 10 2014
STATUS
approved