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.

A036536 Smallest cube containing exactly n 9's.

Original entry on oeis.org

0, 729, 29791, 970299, 994011992, 997002999, 499999005953, 999700029999, 999940001199992, 999970000299999, 991023990975990999, 999997000002999999, 299243659909999996099, 999999700000029999999, 929999949497863992829999, 999100239990997599909999
Offset: 0

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Author

Keywords

Comments

a(n)^(1/3) = A048374(n) is the index of the first occurrence of n in sequence A269249. - M. F. Hasler, Feb 21 2016

Crossrefs

Cf. A048374, A036527 - A036535 for other digits 0 - 8.
Analog for squares: A036516 = A048354^2.

Programs

  • Mathematica
    nsmall = Table[Infinity, 15];
    For[i = 0, i <= 10^6, i++, n0 = Count[IntegerDigits[i^3], 9];
      If[nsmall[[n0 + 1]] > i^3, nsmall[[n0 + 1]] = i^3]];
    Cases[nsmall, ?NumberQ] (* _Robert Price, Mar 20 2020 *)

Formula

a(n) = A048374(n)^3. - M. F. Hasler, Feb 21 2016

Extensions

Extended with a(0) = 0 by M. F. Hasler, Feb 21 2016
a(12)-a(15) from Giovanni Resta, Jun 29 2018

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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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

A048354 a(n)^2 is the smallest square containing exactly n 9's.

Original entry on oeis.org

3, 63, 173, 1414, 17313, 53937, 138923, 953937, 3082207, 31622764, 99849687, 301579177, 3033150173, 14142134563, 141413973847, 543315746063, 3098361825223, 5477225574409, 14139412282687, 314896807700437, 412286308285783, 3147904051904219, 9055381813816577, 311447546136054827, 282841298257395573
Offset: 1

Views

Author

Patrick De Geest, Mar 15 1999

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_]:=Module[{i},i=1;While[DigitCount[i^2][[9]]!=n,i++ ];i]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 23 2006 *)

Extensions

a(13)-a(15) from Jon E. Schoenfield, Jan 24 2009
a(16) from Jon E. Schoenfield, Jan 25 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

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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.