This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A036507 #25 Aug 26 2025 04:54:39
%S A036507 0,100,102400,10000,10240000,1000000,1024000000,100000000,
%T A036507 102400000000,10000000000,10240000000000,1000000000000,
%U A036507 1024000000000000,100000000000000,102400000000000000,10000000000000000,10240000000000000000,1000000000000000000,1024000000000000000000
%N A036507 Smallest square containing exactly n decimal digits '0'.
%F A036507 a(2*n) = 10^(2*n), a(2*n+1) = 1024*10^(2*n) for n >= 1 since 1024 is the smallest square factor that contains a single '0'. - _Georg Fischer_, Jul 03 2023
%F A036507 Sum_{n>=2} 1/a(n) = 1025/101376. - _Amiram Eldar_, Aug 26 2025
%t A036507 nsmall = Table[Infinity, 20];
%t A036507 For[i = 0, i <= 4*10^6, i++, n0 = Count[IntegerDigits[i^2], 0];
%t A036507 If[nsmall[[n0]] > i^2, nsmall[[n0]] = i^2]];
%t A036507 ReplaceAll[nsmall, Infinity -> "?"] (* _Robert Price_, Mar 22 2020 *)
%t A036507 a[n_] := If[OddQ[n], 1024*10^(n-1), 10^n]; a[1] = 0; Array[a, 20] (* _Amiram Eldar_, Aug 26 2025 *)
%Y A036507 Cf. A036508 (digits 1), A036509 (2), A036510 (3), A036511 (4), A036512 (5), A036513 (6), A036514 (7), A036515 (8), A036516 (9).
%K A036507 nonn,base,easy,changed
%O A036507 1,2
%A A036507 _David W. Wilson_