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

%I #25 Apr 28 2023 08:18:06

%S 6,24,489,4569,14129,147984,2149284,25191729,621806289,5259630921,

%T 19998666404,102500044289,3925449108561,13071591635856,42248099518244,

%U 4224809951824400,43007675962234436,506034404021388356,6997839444766224,699783944476622400

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

%H Robert Israel, <a href="/A267032/b267032.txt">Table of n, a(n) for n = 0..998</a>

%H Gwillim Law, <a href="https://gwillim.wordpress.com/2015/12/12/some-sequences/">blog post</a>, Dec. 12, 2015

%F a(n) = A068527(A013715(n)). - _Michel Marcus_, Jan 17 2016

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

%p f:= proc(n) local s;

%p s:= isqrt(10^(2*n+1));

%p if s^2 < 10^(2*n+1) then s:= s+1 fi;

%p s^2 - 10^(2*n+1)

%p end proc:

%p seq(f(n),n=0..40); # _Robert Israel_, Jan 17 2016

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

%o (Python)

%o from math import isqrt

%o def A267032(n): return (isqrt(m:=10**((n<<1)+1))+1)**2-m # _Chai Wah Wu_, Apr 27 2023

%Y Cf. A048761, A068527.

%Y Cf. A238454 (a similar sequence with powers of 2). - _Michel Marcus_, Jan 17 2016

%K nonn

%O 0,1

%A _Gwillim Law_, Jan 09 2016