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.

Previous Showing 11-20 of 20 results.

A269249 Number of times the digit 9 appears in the decimal expansion of n^3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 1, 1, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 2, 3, 0
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 A036535, i.e., A036535(n)^(1/3) = A048374(n) is the index of the first occurrence of n.

Examples

			0^3 = 0, 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, ... and 8^3 = 512 all have a(0) = a(1) = ... = a(8) = 0 digits '9'.
9^3 = 729 has a(9) = 1 digit '9'.

Links

Crossrefs

Cf. A036536 and A036527 - A036535; A048374 and A048365 - A048373.
Analog for the other digits 0, 1, ..., 8: A269250, A269241, A269242, A269243, A269244, A269245, A269246, A269247, A269248.
Analog for squares: A086017 (digit 9) and A086008 - A086016 for digits 0 - 8.

Programs

  • Mathematica
    DigitCount[(Range[0, 100])^3, 10, 9] (* G. C. Greubel, Dec 13 2016 *)
  • PARI
    A269249(n)=#select(t->t==9,digits(n^3))

A048366 a(n)^3 is smallest cube containing exactly n 1's.

Original entry on oeis.org

1, 11, 58, 106, 671, 1041, 10058, 22598, 145981, 480765, 2359231, 10297461, 4836178, 100395471, 465933117, 481182258, 4810215701, 16886336471, 49303833471, 103791158471, 223818432208, 4643311948655, 4809689791471
Offset: 1

Views

Author

Patrick De Geest, Mar 15 1999

Keywords

Links

Crossrefs

Cf. A036528, A048365, A048367, A048368, A048369, A048370, A048371, A048372, A048373, A048374.

Programs

  • Mathematica
    a[n_] := Module[{i}, i = 1; While[DigitCount[i^3][[1]] != 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(23) from Giovanni Resta, Jun 29 2018

A048373 a(n)^3 is smallest cube containing exactly n 8's.

Original entry on oeis.org

2, 42, 92, 436, 942, 2402, 16942, 52942, 266192, 2018892, 3069442, 14242355, 44559402, 207156367, 206524022, 2663151915, 5415821442, 7298885092, 33777876942, 441138374692, 1690359374442, 1316916061361
Offset: 1

Views

Author

Patrick De Geest, Mar 15 1999

Keywords

Links

Crossrefs

Cf. A036535, A048365, A048366, A048367, A048368, A048369, A048370, A048371, A048372, A048374.

Programs

  • Mathematica
    a[n_] := Module[{i = 0}, While[DigitCount[i^3][[8]] != n, i++ ]; i] (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 29 2006 *)

Extensions

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

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

A048368 a(n)^3 is smallest cube containing exactly n 3's.

Original entry on oeis.org

17, 7, 179, 477, 707, 6935, 15477, 44197, 535677, 693368, 2028209, 7566137, 32215777, 62446477, 322024127, 2027400657, 5171307877, 15373346477, 28575396477, 237304541491, 322033146477, 5105022776547, 4536383124177
Offset: 1

Views

Author

Patrick De Geest, Mar 15 1999

Keywords

Examples

			477^3 = 108531333 is the first cube containing four 3's, so a(4) = 477.

Links

Crossrefs

Cf. A036530, A048365, A048366, A048367, A048369, A048370, A048371, A048372, A048373, A048374.

Programs

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

Extensions

a(14)-a(16) from Simon Nickerson (simonn(AT)maths.bham.ac.uk), Aug 12 2005
a(17)-a(20) from Lars Blomberg, Jun 12 2011
a(21)-a(23) from Giovanni Resta, Jun 29 2018

A048369 a(n)^3 is smallest cube containing exactly n 4's.

Original entry on oeis.org

4, 14, 114, 164, 763, 3543, 17066, 13464, 163974, 757364, 3421244, 6727219, 28902604, 35685649, 761777604, 1350780517, 2543012249, 7633715304, 101476238101, 163186746514, 353823251814, 5708006133707
Offset: 1

Views

Author

Patrick De Geest, Mar 15 1999

Keywords

Links

Crossrefs

Cf. A036531, A048365, A048366, A048367, A048368, A048370, A048371, A048372, A048373, A048374.

Programs

  • Mathematica
    nsmall = Table[Infinity, 15];
For[i = 0, i <= 10^6, i++, n0 = Count[IntegerDigits[i^3], 4];
  If[nsmall[[n0]] > i, nsmall[[n0]] = i]];
Cases[nsmall, ?NumberQ] (* _Robert Price, Mar 20 2020 *)

Extensions

a(15)-a(20) from Lars Blomberg, Jun 12 2011
a(21) from Giovanni Resta, Jun 29 2018
a(22) from Giovanni Resta, Mar 23 2020

A048370 a(n)^3 is smallest cube containing exactly n 5's.

Original entry on oeis.org

5, 25, 136, 715, 1526, 11828, 8121, 115798, 319405, 1771087, 2179693, 11665419, 38160335, 176024528, 1367063798, 3257101805, 9109186828, 38598478444, 136736651535, 380814792667, 821922685008
Offset: 1

Views

Author

Patrick De Geest, Mar 15 1999

Keywords

Links

Crossrefs

Cf. A036532, A048365, A048366, A048367, A048368, A048369, A048371, A048372, A048373, A048374.

Programs

  • Mathematica
    nsmall = Table[Infinity, 15];
For[i = 0, i <= 10^6, i++, n0 = Count[IntegerDigits[i^3], 5];
  If[nsmall[[n0]] > i, nsmall[[n0]] = i]];
Cases[nsmall, ?NumberQ] (* _Robert Price, Mar 20 2020 *)

Extensions

a(14) from Michel ten Voorde Jun 13 2003
a(15)-a(20) from Lars Blomberg, Jun 12 2011
a(21) from Giovanni Resta, Jun 29 2018

A048371 a(n)^3 is smallest cube containing exactly n 6's.

Original entry on oeis.org

4, 55, 36, 716, 1188, 4055, 13832, 18821, 190806, 1542023, 3971816, 13881356, 55009989, 154057624, 551727536, 1881662989, 4014051821, 15448244536, 185043243523, 405480132286, 550651031786, 4425284190954, 4881712198556
Offset: 1

Views

Author

Patrick De Geest, Mar 15 1999

Keywords

Links

Crossrefs

Cf. A036533, A048365, A048366, A048367, A048368, A048369, A048370, A048372, A048373, A048374.

Programs

  • Mathematica
    a[n_] := Module[{i = 0}, While[DigitCount[i^3][[6]] != n, i++ ]; i]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 27 2006 *)

Extensions

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

A048372 a(n)^3 is smallest cube containing exactly n 7's.

Original entry on oeis.org

3, 26, 83, 173, 1983, 2953, 19753, 90643, 258999, 426859, 4255753, 13955253, 42111153, 92356426, 425851173, 878398753, 9197190176, 9196397753, 89494606688, 390974932563, 918856391641, 4250703842293
Offset: 1

Views

Author

Patrick De Geest, Mar 15 1999

Keywords

Links

Crossrefs

Cf. A036534, A048365, A048366, A048367, A048368, A048369, A048370, A048371, A048373, A048374.

Programs

  • Mathematica
    a[n_] := Module[{i = 0}, While[DigitCount[i^3][[7]] != n, i++ ]; i]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 27 2006 *)

Extensions

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

A154992 A048473 prefixed by two zeros.

Original entry on oeis.org

0, 0, 1, 5, 17, 53, 161, 485, 1457, 4373, 13121, 39365, 118097, 354293, 1062881, 3188645, 9565937, 28697813, 86093441, 258280325, 774840977, 2324522933, 6973568801, 20920706405, 62762119217, 188286357653, 564859072961
Offset: 0

Views

Author

Paul Curtz, Jan 18 2009

Keywords

Comments

Consider two generic sequences correlated via c(n)=b(n) mod p. The difference d(n)=b(n)-c(n) contains only multiples of p and a(n)=d(n)/p defines another integer sequence. This sequence here takes b(n)=A048473(n) with p=9, such that c(n)=1,5,8,8,8,.. (period 8 continued). Then d(n)= 0,0,9,45,153,477,1449,.. becomes 9 times (two zeros followed by A048473) and division through 9 generates a(n) as the shifted version of b(n)=A048374(n).

Links

Programs

  • Mathematica
    CoefficientList[Series[(x^3 + x^2)/(3*x^2 - 4*x + 1), {x, 0, 50}], x] (* G. C. Greubel, Feb 21 2017 *)
LinearRecurrence[{4,-3},{0,0,1,5},30] (* Harvey P. Dale, May 19 2024 *)
  • PARI
    x='x+O('x^50); Vec((x^3 + x^2)/(3*x^2 - 4*x + 1)) \\ G. C. Greubel, Feb 21 2017

Formula

a(n) = A048473(n-2) = 3*2^(n-2)-1, n>1. - R. J. Mathar, Jan 23 2009
G.f.: (x^3 + x^2)/(3*x^2 - 4*x + 1). - Alexander R. Povolotsky, Feb 21 2009

Extensions

Edited and extended by R. J. Mathar, Jan 23 2009
Previous Showing 11-20 of 20 results.

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