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 1-5 of 5 results.

A269242 Number of times the digit 2 appears in the decimal expansion of n^3.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 2, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 1, 2, 2, 1, 0, 1, 1, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1
Offset: 0

Views

Author

M. F. Hasler, Feb 20 2016

Keywords

Comments

The cubes corresponding to the first occurrence of 1, 2, 3, ... are listed in A036529, i.e., A036529(n)^(1/3) = A048367(n) is the index of the first occurrence of n.

Examples

			0^3 = 0 has a(0) = 0 digits '2'.
1^3 = 1 has a(1) = 0 digits '2'.
2^3 = 8 has a(2) = 0 digits '2'.
3^3 = 27 has a(3) = 1 digits '2'.
4^3 = 64 has a(4) = 0 digits '2'.
5^3 = 125 has a(5) = 1 digit '2'.
28^3 = 21952 is the least cube which has a(28) = 2 digits '2'.

Links

Crossrefs

Cf. A036529 and A036527 - A036536; A048367 and A048365 - A048374.
Analog for the other digits 0, 1, ..., 9: A269250, A269241, A269242, A269243, A269244, A269245, A269246, A269247, A269248, A269249.
Analog for squares: A086010 (digit 2), and A086008 - A086017 for digits 0 - 9.

Programs

  • Magma
    [Multiplicity(Intseq(n^3),2): n in [0..100]]; // Marius A. Burtea, Jan 26 2020
  • Maple
    seq(numboccur(2,convert(n^3,base,10)),n=0..100); # Robert Israel, Jan 26 2020
  • Mathematica
    Table[DigitCount[n^3, 10, 2], {n, 0, 100}] (* Robert Price, Mar 21 2020 *)
  • PARI
    A269242(n)=#select(t->t==2,digits(n^3))

A048367 a(n)^3 is smallest cube containing exactly n 2's.

Original entry on oeis.org

3, 28, 138, 587, 612, 2824, 27654, 29603, 131468, 1312748, 1616488, 2811574, 49629974, 139796852, 281986403, 1264554822, 6146857824, 16162692208, 60598584603, 229717543765, 606069984352, 2811738231378, 5869673191741
Offset: 1

Views

Author

Patrick De Geest, Mar 15 1999

Keywords

Links

Crossrefs

Cf. A036529, A048365, A048366, A048368, A048369, A048370, A048371, A048372, A048373, A048374.

Programs

  • Mathematica
    a[n_] := Module[{i}, i = 1; While[DigitCount[i^3][[2]] != n, i++ ]; i]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 23 2006 *)

Extensions

a(14) from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 23 2006
a(15)-a(20) from Lars Blomberg, Jun 12 2011
a(21)-a(22) from Giovanni Resta, Jun 29 2018
a(23) from Giovanni Resta, Mar 27 2020

A036528 Smallest cube containing exactly n 1's.

Original entry on oeis.org

0, 1, 1331, 195112, 1191016, 302111711, 1128111921, 1017501115112, 11540111711192, 3110921146111141, 111121611171697125, 13131411119181123391, 1091919111651131183181, 113111518118141111752, 1011911111044153611072111, 101151130119180103111112613
Offset: 0

Views

Author

David W. Wilson

Keywords

Comments

a(n)^(1/3) = A048366(n) is the index of the first occurrence of n in sequence A269241. - M. F. Hasler, Feb 21 2016

Links

Crossrefs

Cf. A048366, A036527, A036529, A036530, A036531, A036532, A036533, A036534, A036535, A036536.

Programs

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

Formula

a(n) = A048366(n)^3. - M. F. Hasler, Feb 21 2016

Extensions

a(12)-a(15) from Giovanni Resta, Jun 29 2018

A036530 Smallest cube containing exactly n 3's.

Original entry on oeis.org

0, 4913, 343, 5735339, 108531333, 353393243, 333533450375, 3707322336333, 86333306433373, 153712433903333733, 333343033492332032, 8343304933332333329, 433134325352337333353, 33435346723033333302433, 243513939323833732333333, 33393753313938361233336383
Offset: 0

Views

Author

David W. Wilson

Keywords

Comments

a(n)^(1/3) = A048368(n) is the index of the first occurrence of n in sequence A269243. - M. F. Hasler, Feb 21 2016

Links

Crossrefs

Cf. A048368, A036527, A036528, A036529, A036531, A036532, A036533, A036534, A036535, A036536.

Programs

  • Mathematica
    Table[SelectFirst[Range[2100000]^3,DigitCount[#,10,3]==n&],{n,11}] (* The program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, Oct 24 2015 *)

Formula

a(n) = A048368(n)^3. - M. F. Hasler, Feb 21 2016

Extensions

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

A036531 Smallest cube containing exactly n 4's.

Original entry on oeis.org

0, 64, 2744, 1481544, 4410944, 444194947, 44474744007, 4970444443496, 2440744441344, 4408846444574424, 434424163454644544, 40045354844444494784, 304443494462464444459, 24144094248434404444864, 45444444436448021414449, 442063442345444443482444864
Offset: 0

Views

Author

David W. Wilson

Keywords

Comments

a(n)^(1/3) = A048369(n) is the index of the first occurrence of n in sequence A269244. - M. F. Hasler, Feb 21 2016

Links

Crossrefs

Cf. A048369, A036527, A036528, A036529, A036530, A036532, A036533, A036534, A036535, A036536.

Programs

  • Mathematica
    nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, n0 = Count[IntegerDigits[i^3], 4];
  If[nsmall[[n0 + 1]] > i^3, nsmall[[n0 + 1]] = i^3]];
Cases[nsmall, ?NumberQ] (* _Robert Price, Mar 21 2020 *)

Formula

a(n) = A048369(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
Showing 1-5 of 5 results.

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