A086016 -id:A086016 - cp's OEIS frontend

A086008 Number of 0's in decimal expansion of n^2.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 4, 2, 2, 2, 1

Offset: 0

Jason Earls, Jul 07 2003

			10^2 = 100, so a(10)=2 and 32^2 = 1024, so a(32)=1.

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

Cf. 1's A086009, 2's A086010, 3's A086011, 4's A086012, 5's A086013, 6's A086014, 7's A086015, 8's A086016, 9's A086017.

Cf. A269250 for the n^3 analog.

DigitCount[(Range[0, 100])^2, 10, 0] (* G. C. Greubel, Dec 13 2016 *)

A086008(n)=!n+#select(d->!d,digits(n^2)) \\ M. F. Hasler, Feb 21 2016

A086017 Number of 9's in decimal expansion of n^2.

Original entry on oeis.org

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

Offset: 0

Jason Earls, Jul 07 2003

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

Cf. 0's A086008, 1's A086009, 2's A086010, 3's A086011, 4's A086012, 5's A086013, 6's A086014, 7's A086015, 8's A086016.

Cf. A269249 for the n^3 analog.

DigitCount[(Range[0, 100])^2, 10, 9] (* G. C. Greubel, Dec 13 2016 *)

A086017(n)=#select(d->d==9,digits(n^2)) \\ M. F. Hasler, Feb 21 2016

A086009 Number of 1's in decimal expansion of n^2.

Original entry on oeis.org

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

Offset: 0

Jason Earls, Jul 07 2003

			4^2 = 16, so a(4)=1 and 11^2 = 121, so a(11)=2.

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

Cf. 0's A086008, 2's A086010, 3's A086011, 4's A086012, 5's A086013, 6's A086014, 7's A086015, 8's A086016, 9's A086017.

Cf. A269241 for the n^3 analog.

DigitCount[(Range[0, 100])^2, 10, 1] (* G. C. Greubel, Dec 13 2016 *)

A086009(n)=#select(d->d==1,digits(n^2)) \\ M. F. Hasler, Feb 21 2016

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))
```

A086010 Number of 2's in decimal expansion of n^2.

Original entry on oeis.org

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

Offset: 0

Jason Earls, Jul 07 2003

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

Cf. 0's A086008, 1's A086009, 3's A086011, 4's A086012, 5's A086013, 6's A086014, 7's A086015, 8's A086016, 9's A086017.

Cf. A269242 for the n^3 analog.

DigitCount[(Range[0, 100])^2, 10, 2] (* G. C. Greubel, Dec 13 2016 *)

A086010(n)=#select(d->d==2,digits(n^2)) \\ M. F. Hasler, Feb 21 2016

A086011 Number of 3's in decimal expansion of n^2.

Original entry on oeis.org

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

Offset: 0

Jason Earls, Jul 07 2003

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

Cf. 0's A086008, 1's A086009, 2's A086010, 4's A086012, 5's A086013, 6's A086014, 7's A086015, 8's A086016, 9's A086017.

Cf. A269243 for the n^3 analog.

DigitCount[(Range[0, 100])^2, 10, 3] (* G. C. Greubel, Dec 13 2016 *)

A086011(n)=#select(d->d==3,digits(n^2)) \\ M. F. Hasler, Feb 21 2016

A086012 Number of 4's in decimal expansion of n^2.

Original entry on oeis.org

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

Offset: 0

Jason Earls, Jul 07 2003

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

Cf. 0's A086008, 1's A086009, 2's A086010, 3's A086011, 5's A086013, 6's A086014, 7's A086015, 8's A086016, 9's A086017.

Cf. A269244 for the n^3 analog.

DigitCount[(Range[0, 100])^2, 10, 4] (* G. C. Greubel, Dec 13 2016 *)

A086012(n)=#select(d->d==4,digits(n^2)) \\ M. F. Hasler, Feb 21 2016

A086013 Number of 5's in decimal expansion of n^2.

Original entry on oeis.org

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

Offset: 0

Jason Earls, Jul 07 2003

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

Cf. 0's A086008, 1's A086009, 2's A086010, 3's A086011, 4's A086012, 6's A086014, 7's A086015, 8's A086016, 9's A086017.

Cf. A269245 for the n^3 analog.

DigitCount[(Range[0,110])^2,10,5] (* Harvey P. Dale, Jul 26 2016 *)

A086013(n)=#select(d->d==5,digits(n^2)) \\ M. F. Hasler, Feb 21 2016

A086014 Number of 6's in decimal expansion of n^2.

Original entry on oeis.org

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

Offset: 0

Jason Earls, Jul 07 2003

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

Cf. 0's A086008, 1's A086009, 2's A086010, 3's A086011, 4's A086012, 5's A086013, 7's A086015, 8's A086016, 9's A086017.

Cf. A269246 for the n^3 analog.

Table[DigitCount[n^2,10,6],{n,0,110}] (* Harvey P. Dale, May 24 2014 *)

A086014(n)=#select(d->d==6,digits(n^2)) \\ M. F. Hasler, Feb 21 2016

cp's OEIS Frontend

A086008 Number of 0's in decimal expansion of n^2.

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A086017 Number of 9's in decimal expansion of n^2.

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A086009 Number of 1's in decimal expansion of n^2.

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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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A086010 Number of 2's in decimal expansion of n^2.

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A086011 Number of 3's in decimal expansion of n^2.

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A086012 Number of 4's in decimal expansion of n^2.

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A086013 Number of 5's in decimal expansion of n^2.

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