A036534 -id:A036534 - cp's OEIS frontend

A269247 Number of times the digit 7 appears in the decimal expansion of n^3.

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

Offset: 0

M. F. Hasler, Feb 20 2016

The cubes corresponding to the first occurrence of 1, 2, 3, ... are listed in A036534, i.e., A036534(n)^(1/3) = A048372(n) is the index of the first occurrence of n.

			0^3 = 0, 1^3 = 1, 2^3 = 8 and 4^3 = 64 all have a(0) = a(1) = a(2) = a(4) = 0 digits '7'.
3^3 = 27 has a(3) = 1 digit '7'.

Cf. A036534 and A036527 - A036536; A048372 and A048365 - A048374.
Analog for the other digits 0, 1, ..., 9: A269250, A269241, A269242, A269243, A269244, A269245, A269246, A269247, A269248, A269249.
Analog for squares: A086015 (digit 7), and A086008 - A086017 for digits 0 - 9.

Table[DigitCount[n^3, 10, 7], {n, 0, 100}] (* Robert Price, Mar 21 2020 *)

PARI
```
A269247(n)=#select(t->t==7,digits(n^3))
```

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

Patrick De Geest, Mar 15 1999

Eric Weisstein's World of Mathematics, Cubic Number

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

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 *)

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

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

cp's OEIS Frontend

A269247 Number of times the digit 7 appears in the decimal expansion of n^3.

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