A036507 - OEIS

%I #16 Jul 03 2023 08:01:54

%S 0,100,102400,10000,10240000,1000000,1024000000,100000000,

%T 102400000000,10000000000,10240000000000,1000000000000,

%U 1024000000000000,100000000000000,102400000000000000,10000000000000000

%N Smallest square containing exactly n decimal digits '0'.

%F a(2*n) = 10^(2*n), a(2*n+1) = 1024*10^(2*n) for k >= 1 since 1024 is the smallest square factor that contains a single '0'. - _Georg Fischer_, Jul 03 2023

%t nsmall = Table[Infinity, 20];

%t For[i = 0, i <= 4*10^6, i++, n0 = Count[IntegerDigits[i^2], 0];

%t   If[nsmall[[n0]] > i^2, nsmall[[n0]] = i^2]];

%t ReplaceAll[nsmall, Infinity -> "?"] (* _Robert Price_, Mar 22 2020 *)

%Y Cf. A036508 (digits 1), A036509 (2), A036510 (3), A036511 (4), A036512 (5), A036513 (6), A036514 (7), A036515 (8), A036516 (9).

%K nonn,base

%O 1,2

%A _David W. Wilson_