A036531 -id:A036531 - cp's OEIS frontend

A269244 Number of times the digit 4 appears in the decimal expansion of n^3.

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

Offset: 0

M. F. Hasler, Feb 20 2016

The cubes corresponding to the first occurrence of 1, 2, 3, ... are listed in A036531, i.e., A036531(n)^(1/3) = A048369(n) is the index of the first occurrence of n.

			0^3 = 0, 1^3 = 1, 2^3 = 8 and 3^3 = 27 all have a(0) = a(1) = a(2) = a(3) = 0 digits '4'.
4^3 = 64 has a(4) = 1 digit '4'.
14^3 = 2744 has a(14) = 2 digits '4'.

Cf. A036531 and A036527 - A036536; A048369 and A048365 - A048374.
Analog for the other digits 0, 1, ..., 9: A269250, A269241, A269242, A269243, A269244, A269245, A269246, A269247, A269248, A269249.
Analog for squares: A086012 (digit 4), and A086008 - A086017 for digits 0 - 9.

Table[DigitCount[n^3, 10, 4], {n, 0, 100}] (* Robert Price, Mar 21 2020 *)

PARI
```
A269244(n)=#select(t->t==4,digits(n^3))
```

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

Patrick De Geest, Mar 15 1999

Eric Weisstein's World of Mathematics, Cubic Number

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

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 *)

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

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

cp's OEIS Frontend

A269244 Number of times the digit 4 appears in the decimal expansion of n^3.

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