A267032 Difference between smallest integer square >= 10^(2*n+1) and 10^(2*n+1).

6, 24, 489, 4569, 14129, 147984, 2149284, 25191729, 621806289, 5259630921, 19998666404, 102500044289, 3925449108561, 13071591635856, 42248099518244, 4224809951824400, 43007675962234436, 506034404021388356, 6997839444766224, 699783944476622400

Offset: 0

Author

Gwillim Law, Jan 09 2016

Keywords

• nonn

Examples

			a(0) = 6 = 4^2 - 10; a(1) = 24 = 32^2 - 1000.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..998
• Gwillim Law, blog post, Dec. 12, 2015

Crossrefs

Cf. A048761, A068527.

Cf. A238454 (a similar sequence with powers of 2). - Michel Marcus, Jan 17 2016

Programs

Maple

f:= proc(n) local s;
  s:= isqrt(10^(2*n+1));
  if s^2 < 10^(2*n+1) then s:= s+1 fi;
  s^2 - 10^(2*n+1)
end proc:
seq(f(n),n=0..40); # Robert Israel, Jan 17 2016

Mathematica

dsis[n_]:=Module[{c=10^(2n+1)},(Floor[Sqrt[c]]+1)^2-c]; Array[dsis,20,0] (* Harvey P. Dale, Apr 27 2019 *)

Python

from math import isqrt
def A267032(n): return (isqrt(m:=10**((n<<1)+1))+1)**2-m # Chai Wah Wu, Apr 27 2023

Formula

a(n) = A068527(A013715(n)). - Michel Marcus, Jan 17 2016