OFFSET
1,2
COMMENTS
The equation 16*t^2 - 32*t + k^2 + 8*k - 8*k*t + 16 always produces a square, for any number n, with any t and k (i.e., t can be incremented and a corresponding k value is produced).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ 2*sqrt(n). - Charles R Greathouse IV, Oct 14 2016
a(n) = n - (floor(sqrt(n-1))-1)^2. - Charles R Greathouse IV, Oct 14 2016
a(n) = n - ceiling(sqrt(n) - 2)^2. - Vincenzo Librandi, Nov 06 2016
EXAMPLE
n = 3, f(n) = 3; n = 11, f(n) = 7; n = 64, f(n) = 28; n = 103, f(n) = 22; n=208, f(n)= 39.
MAPLE
seq(n-ceil(sqrt(n)-2)^2, n = 1 .. 64); # Ridouane Oudra, Jun 11 2019
MATHEMATICA
Table[Function[t, Function[k, Sqrt[16 t^2 - 32 t + k^2 + 8 k - 8 k t + 16]][t^2 - n]]@ Ceiling@ Sqrt@ n, {n, 64}] (* or *)
Table[n - Ceiling[Sqrt[n] - 2]^2, {n, 64}] (* Michael De Vlieger, Nov 06 2016 *)
PROG
(PARI) a(n) = n - (sqrtint(n-1)-1)^2 \\ Charles R Greathouse IV, Oct 14 2016
(Magma) [n-Ceiling(Sqrt(n)-2)^2: n in [1..80]]; // Vincenzo Librandi, Nov 06 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Joseph Foley, Oct 14 2016
STATUS
approved