A036507
Smallest square containing exactly n decimal digits '0'.
Original entry on oeis.org
0, 100, 102400, 10000, 10240000, 1000000, 1024000000, 100000000, 102400000000, 10000000000, 10240000000000, 1000000000000, 1024000000000000, 100000000000000, 102400000000000000, 10000000000000000, 10240000000000000000, 1000000000000000000, 1024000000000000000000
Offset: 1
-
nsmall = Table[Infinity, 20];
For[i = 0, i <= 4*10^6, i++, n0 = Count[IntegerDigits[i^2], 0];
If[nsmall[[n0]] > i^2, nsmall[[n0]] = i^2]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)
a[n_] := If[OddQ[n], 1024*10^(n-1), 10^n]; a[1] = 0; Array[a, 20] (* Amiram Eldar, Aug 26 2025 *)
A048347
a(n)^2 is the smallest square containing exactly n 2's.
Original entry on oeis.org
5, 15, 149, 1415, 4585, 14585, 105935, 364585, 3496101, 4714045, 34964585, 149305935, 1490725415, 4714469665, 1490711985, 149071333335, 1105537083332, 1489973900149, 15106363633335, 47140462469223, 450246846657722, 1490713327333335, 4714049454791668, 47129833685493335, 27788886667555111
Offset: 1
From _Jon E. Schoenfield_, Dec 25 2008: (Start)
a(16) = 149071333335 = sqrt(22222262422274682222225);
a(17) = 1105537083332 = sqrt(1222212242622225512222224);
a(18) = 1489973900149 = sqrt(2220022223125222222222201). (End)
From _Giovanni Resta_, Jul 27 2018: (Start)
a(19) = 15106363633335 = sqrt(228202222222546222323222225);
a(20) = 47140462469223 = sqrt(2222223201812222222222223729). (End)
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a[n_] := Block[{k=1}, While[DigitCount[k^2, 10, 2] != n, k++]; k]; Array[a, 7] (* Giovanni Resta, Jul 27 2018 *)
a(13)-a(15) from
Max Alekseyev, Oct 20 2008, Nov 10 2008, Dec 05 2008
A137434
a(n) = smallest square containing n copies of the same nonzero digit.
Original entry on oeis.org
1, 121, 1444, 44944, 6441444, 47444544, 4434494464, 44424414441, 1113111511681, 22222220262025, 444431244445444, 22292262226224225, 441544444344443449, 1113101111111117041, 2222222222222640225, 11111119101145491111121
Offset: 1
a(9) = 1113111511681 because there is no smaller square number with 9 copies of the same nonzero digit. a(9) has 9 1's.
Showing 1-3 of 3 results.