cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

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

Views

Author

Keywords

Crossrefs

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

Programs

  • Mathematica
    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 *)

Formula

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
Sum_{n>=2} 1/a(n) = 1025/101376. - 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

Views

Author

Patrick De Geest, Mar 15 1999

Keywords

Examples

			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)
		

Crossrefs

Programs

  • Mathematica
    a[n_] := Block[{k=1}, While[DigitCount[k^2, 10, 2] != n, k++]; k]; Array[a, 7] (* Giovanni Resta, Jul 27 2018 *)

Extensions

a(13)-a(15) from Max Alekseyev, Oct 20 2008, Nov 10 2008, Dec 05 2008
a(16)-a(18) from Jon E. Schoenfield, Dec 25 2008
a(19)-a(20) from Giovanni Resta, Jul 27 2018
a(21)-a(25) from Max Alekseyev, Mar 06 2025

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

Views

Author

Randy L. Ekl, Apr 17 2008

Keywords

Examples

			a(9) = 1113111511681 because there is no smaller square number with 9 copies of the same nonzero digit. a(9) has 9 1's.
		

Crossrefs

Extensions

Edited by N. J. A. Sloane at the suggestion of Jon E. Schoenfield, Jan 11 2009
a(12)-a(15) from Jon E. Schoenfield, Jan 14 2009
a(16) from Jon E. Schoenfield, Jan 17 2009
Showing 1-3 of 3 results.