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