A036535 -id:A036535 - cp's OEIS frontend

A036536 Smallest cube containing exactly n 9's.

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

Offset: 0

David W. Wilson

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

Giovanni Resta, Table of n, a(n) for n = 0..23

Cf. A048374, A036527 - A036535 for other digits 0 - 8.

Analog for squares: A036516 = A048354^2.

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 *)

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

Extended with a(0) = 0 by M. F. Hasler, Feb 21 2016

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

A269248 Number of times the digit 8 appears in the decimal expansion of n^3.

Original entry on oeis.org

0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 3, 1, 2, 1, 2, 0, 0, 0, 0

Offset: 0

M. F. Hasler, Feb 20 2016

The cubes corresponding to the first occurrence of 1, 2, 3, ... are listed in A036535, i.e., A036535(n)^(1/3) = A048373(n) is the index of the first occurrence of n.

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

Cf. A036535 and A036527 - A036536; A048373 and A048365 - A048374.
Analog for other digits 0, 1, ..., 7, 9: A269250, A269241, A269242, A269243, A269244, A269245, A269246, A269247, A269249.
Analog for squares: A086016, and A086008 - A086017 for digits 0 - 9.

Table[DigitCount[n^3, 10, 8], {n, 0, 100}] (* Robert Price, Mar 21 2020 *)

PARI
```
A269248(n)=#select(t->t==8,digits(n^3))
```

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

M. F. Hasler, Feb 20 2016

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.

			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'.

G. C. Greubel, Table of n, a(n) for n = 0..1000

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.

DigitCount[(Range[0, 100])^3, 10, 9] (* G. C. Greubel, Dec 13 2016 *)

PARI
```
A269249(n)=#select(t->t==9,digits(n^3))
```

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

Patrick De Geest, Mar 15 1999

Eric Weisstein's World of Mathematics, Cubic Number

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

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 *)

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

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

David W. Wilson

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

Giovanni Resta, Table of n, a(n) for n = 0..23

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

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 *)

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

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

A036529 Smallest cube containing exactly n 2's.

Original entry on oeis.org

0, 27, 21952, 2628072, 202262003, 229220928, 22521332224, 21148222722264, 25942222239227, 2272271222935232, 2262268226562252992, 4223937222222326272, 22225347273222227224, 122245292222422449622424, 2732072222242422541222208, 22422524292920620222272827

Offset: 0

David W. Wilson

a(n)^(1/3) = A048367(n) is the index of the first occurrence of n in sequence A269242. - M. F. Hasler, Feb 21 2016

Giovanni Resta, Table of n, a(n) for n = 0..23

Cf. A048367, A036527, A036528, A036530, A036531, A036532, A036533, A036534, A036535, A036536.

nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, n0 = Count[IntegerDigits[i^3], 2];
  If[nsmall[[n0 + 1]] > i^3, nsmall[[n0 + 1]] = i^3]];
Cases[nsmall, ?NumberQ] (* _Robert Price, Mar 20 2020 *)

a(n) = A048367(n)^3. - M. F. Hasler, Feb 21 2016

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

David W. Wilson

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

Giovanni Resta, Table of n, a(n) for n = 0..23

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

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 *)

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

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

David W. Wilson

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

Giovanni Resta, Table of n, a(n) for n = 0..22

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

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 *)

a(n) = A048369(n)^3. - M. F. Hasler, Feb 21 2016

Extended with a(0) = 0 by M. F. Hasler, Feb 21 2016

a(11)-a(15) from Giovanni Resta, Jun 29 2018

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A036536 Smallest cube containing exactly n 9's.

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A269248 Number of times the digit 8 appears in the decimal expansion of n^3.

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

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

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A036528 Smallest cube containing exactly n 1's.

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A036529 Smallest cube containing exactly n 2's.

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A036530 Smallest cube containing exactly n 3's.

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A036531 Smallest cube containing exactly n 4's.

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