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 1-4 of 4 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

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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

A036534 Smallest cube containing exactly n 7's.

Original entry on oeis.org

0, 27, 17576, 571787, 5177717, 7797729087, 25750777177, 7707245470777, 744736797077707, 17373777757776999, 77777383297757779, 77077787864771842777, 2717772770751727979277, 74677779777959671778577, 787773477172377877676776, 77227778717777797207914717
Offset: 0

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Author

Keywords

Comments

a(n)^(1/3) = A048372(n) is the index of the first occurrence of n in sequence A269247. - M. F. Hasler, Feb 21 2016

Crossrefs

Cf. A048372, A036527 - A036536 for other digits 0 - 9.
Analog for squares: A036514 = A048352^2.

Programs

  • Mathematica
    nsmall = Table[Infinity, 20];
    For[i = 0, i <= 10^6, i++, n0 = Count[IntegerDigits[i^3], 7];
      If[nsmall[[n0 + 1]] > i^3, nsmall[[n0 + 1]] = i^3]];
    Cases[nsmall, ?NumberQ] (* _Robert Price, Mar 21 2020 *)

Formula

a(n) = A048372(n)^3. - M. F. Hasler, Feb 21 2016

Extensions

Extended with a(0) = 0 by M. F. Hasler, Feb 21 2016
a(11)-a(15) from Giovanni Resta, Jun 29 2018

A048352 a(n)^2 is the smallest square containing exactly n 7's.

Original entry on oeis.org

24, 76, 424, 3576, 8819, 88924, 278874, 2116076, 8819154, 61463576, 277450424, 526087234, 1943470576, 21858013924, 199694210926, 260341642412, 3574601764924, 11156736878576, 27180356468924, 275640849218286, 1130388343790654, 8818036509210958, 57251968301165924, 75972671255970576, 841288938282667412
Offset: 1

Views

Author

Patrick De Geest, Mar 15 1999

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := Module[{i = 1}, While[DigitCount[i^2][[7]] != n, i++ ]; i]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 22 2006 *)

Extensions

a(13)-a(16) from Jon E. Schoenfield, Jan 24 2009
a(17)-a(19) from Giovanni Resta, Jul 27 2018
a(20)-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 1-4 of 4 results.