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 1-10 of 10 results.

A048355 a(n) is the index of the smallest triangular number containing exactly n 0's.

Original entry on oeis.org

0, 24, 200, 775, 2000, 10000, 20000, 100000, 200000, 1000000, 2000000, 10000000, 20000000, 100000000, 200000000, 1000000000, 2000000000, 10000000000, 20000000000, 100000000000, 200000000000, 1000000000000, 2000000000000, 10000000000000, 20000000000000, 100000000000000
Offset: 1

Views

Author

Patrick De Geest, Mar 15 1999

Keywords

Examples

			From _Bernard Schott_, Mar 04 2019: (Start)
a(2) = 24: T(24) = 300 which contains exactly two 0's.
a(6) = 10000: T(10000) = 50005000 which contains exactly six 0's.
a(7) = 20000: T(20000) = 200010000 which contains exactly seven 0's.
(End)

Links

Crossrefs

Cf. A000217, A036517.

Programs

  • Mathematica
    nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];
  n0 = Count[IntegerDigits[p], 0];
  If[nsmall[[n0]] > i, nsmall[[n0]] = i]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)
LinearRecurrence[{0,10},{0,24,200,775,2000,10000},30] (* Harvey P. Dale, Jul 26 2024 *)
  • PARI
    Vec(x^2*(24 + 200*x + 535*x^2 + 2250*x^4) / (1 - 10*x^2) + O(x^30)) \\ Colin Barker, Mar 25 2020

Formula

From Bernard Schott, Mar 04 2019: (Start)
for n odd >= 5, a(n) = 2 * 10^((n+1)/2),
for n even >= 6, a(n) = 10^((n+2)/2).
(End)
From Colin Barker, Mar 25 2020: (Start)
G.f.: x^2*(24 + 200*x + 535*x^2 + 2250*x^4) / (1 - 10*x^2).
a(n) = 10*a(n-2) for n>4.
(End)

Extensions

a(16)-a(19) from Lars Blomberg, May 13 2011
a(20)-a(26) from Chai Wah Wu, Mar 04 2019

A036526 Smallest triangular number containing exactly n 9's.

Original entry on oeis.org

91, 990, 199396, 998991, 399949903, 2919969990, 39999939903, 999999911791, 9999192996990, 499798990999990, 99597939989199996, 999699998689998991, 19699899919999499091, 999532899999499099996, 999999859999976929990, 199793999409939999989991, 138999999499599999199995, 99996999694999999299662991
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A048364, A036517-A036525.

Programs

  • Mathematica
    nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];
  n0 = Count[IntegerDigits[p], 9];
  If[nsmall[[n0]] > p, nsmall[[n0]] = p]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)

Extensions

a(12)-a(18) from Giovanni Resta, Oct 30 2019

A036521 Smallest triangular number containing exactly n 4's.

Original entry on oeis.org

45, 4465, 144453, 544446, 427444941, 414446445, 4440447441, 444344944456, 4404424444435, 1046444944404441, 14546344444444945, 441441444448564440, 4445444444946443841, 444438244043444444046, 4444844454444484014645, 44641424644444444411441, 4024414288444444444404441, 44448461444441444448442420
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A048359, A036517-A036526.

Programs

  • Mathematica
    nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];
  n0 = Count[IntegerDigits[p], 4];
  If[nsmall[[n0]] > p, nsmall[[n0]] = p]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)

Extensions

a(12)-a(18) from Giovanni Resta, Oct 30 2019

A036525 Smallest triangular number containing exactly n 8's.

Original entry on oeis.org

28, 3828, 48828, 828828, 55888878, 3288888856, 78888885078, 388884828828, 13889888887878, 28888888883865, 8980885988888880, 88838888988888990, 983888888888812878, 8838888986888887878, 894885888888885888855, 78888888822845888188878, 1888886085781088888888878, 18788848888888828885888126
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A048363, A036517-A036526.

Programs

  • Mathematica
    nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];
  n0 = Count[IntegerDigits[p], 8];
  If[nsmall[[n0]] > p, nsmall[[n0]] = p]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)

Extensions

a(13)-a(18) from Giovanni Resta, Oct 30 2019

A036518 Smallest triangular number containing exactly n 1's.

Original entry on oeis.org

1, 171, 1711, 105111, 1188111, 18111171, 1111160511, 11161151121, 111111101310, 11311511141161, 121111912011111, 11111811011411671, 11101111131911151, 11111111111113201, 111111312111373411111, 1119711111215111121171, 111112117111126711111195, 1141011111112731111616111
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A048356, A036517-A036526.

Programs

  • Mathematica
    nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];
  n0 = Count[IntegerDigits[p], 1];
  If[nsmall[[n0]] > p, nsmall[[n0]] = p]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)
Module[{nn=5*10^6,tr},tr={#,DigitCount[#,10,1]}&/@Accumulate[Range[ nn]]; Table[ SelectFirst[tr,#[[2]]==k&],{k,10}]][[;;,1]] (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Sep 01 2024 *)

Formula

a(n) = A000217(A048356(n)). - Michel Marcus, Aug 12 2014

Extensions

Definition clarified by Robert Israel, Aug 10 2014
a(15)-a(16) from A048356 by Michel Marcus, Aug 12 2014
a(17)-a(18) from Giovanni Resta, Oct 30 2019

A036519 Smallest triangular number containing exactly n 2's.

Original entry on oeis.org

21, 1225, 23220, 212226, 22121226, 2202322528, 21222223210, 202222242820, 22122952222920, 229222922294226, 2221228522222920, 222322222025202925, 222212284222222920, 22222122841222222920, 2092226022222222442221, 22222222042522220020225, 622222207421222222222253, 22222212062122272422225226
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A048357, A036517-A036526.

Programs

  • Mathematica
    nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];
  n0 = Count[IntegerDigits[p], 2];
  If[nsmall[[n0]] > p, nsmall[[n0]] = p]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)

Extensions

a(12)-a(18) from Giovanni Resta, Oct 30 2019

A036520 Smallest triangular number containing exactly n 3's.

Original entry on oeis.org

3, 3003, 33153, 3303735, 333336, 333039336, 13333363350, 330335331336, 3033333513330, 303313733373336, 30333330330333465, 313631353332333336, 330332337333331336, 3333043333303433331, 3333333330453337336653, 30733333373333335323321, 330332334339335333331336, 33033333933433336339893330
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A048358, A036517-A036526.

Programs

  • Mathematica
    nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];
  n0 = Count[IntegerDigits[p], 3];
  If[nsmall[[n0]] > p, nsmall[[n0]] = p]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)

Extensions

a(12)-a(18) from Giovanni Resta, Oct 30 2019

A036522 Smallest triangular number containing exactly n 5's.

Original entry on oeis.org

15, 55, 5565, 255255, 12552555, 585555531, 5355555765, 50525595555, 5258558551555, 555595555515, 1551745755555555, 39355555555552515, 552550545955255555, 13555559555595513555, 455557505555605555585, 5555558514557555255755, 555457555855555784555355, 505555585555455555505395
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A048360, A036517-A036526.

Programs

  • Mathematica
    nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];
  n0 = Count[IntegerDigits[p], 5];
  If[nsmall[[n0]] > p, nsmall[[n0]] = p]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)

Extensions

a(13)-a(18) from Giovanni Resta, Oct 30 2019

A036523 Smallest triangular number containing exactly n 6's.

Original entry on oeis.org

6, 66, 666, 66066, 5666661, 36666766, 646686666, 77666666626, 4666660668676, 66488766666666, 6666063656661696, 6666664664655666, 666416695266666666, 56666136666666763866, 626646696666896766666, 11666966196628666666666, 66666666636866637006666, 2626660686666666671166666
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A048361, A036517-A036526.

Programs

  • Mathematica
    nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];
  n0 = Count[IntegerDigits[p], 6];
  If[nsmall[[n0]] > p, nsmall[[n0]] = p]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)

Extensions

a(13)-a(18) from Giovanni Resta, Oct 30 2019

A036524 Smallest triangular number containing exactly n 7's.

Original entry on oeis.org

78, 1770, 72771, 6787770, 37779778, 2476777771, 7477727778, 7077757275771, 27778877747778, 177775772774775, 7777755777787716, 172777077787777785, 7987777777779277726, 177577777275777787371, 377679777777377717778, 77773137747757777775775, 777367777737777774977796, 67775787670776777773777778
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A048362, A036517-A036526.

Programs

  • Mathematica
    nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, p = PolygonalNumber[i];
  n0 = Count[IntegerDigits[p], 7];
  If[nsmall[[n0]] > p, nsmall[[n0]] = p]];
ReplaceAll[nsmall, Infinity -> "?"] (* Robert Price, Mar 22 2020 *)

Extensions

a(13)-a(18) from Giovanni Resta, Oct 30 2019
Showing 1-10 of 10 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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