A086010 -id:A086010 - 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

A086016 Number of 8's in decimal expansion of n^2.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 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, 6's A086014, 7's A086015, 9's A086017.

Cf. A269248 for the n^3 analog.

DigitCount[(Range[0, 100])^2, 10, 8] (* G. C. Greubel, Dec 13 2016 *)

A086016(n)=#select(d->d==8,digits(n^2)) \\ M. F. Hasler, Feb 21 2016

A269242 Number of times the digit 2 appears in the decimal expansion of n^3.

Original entry on oeis.org

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

Offset: 0

M. F. Hasler, Feb 20 2016

The cubes corresponding to the first occurrence of 1, 2, 3, ... are listed in A036529, i.e., A036529(n)^(1/3) = A048367(n) is the index of the first occurrence of n.

			0^3 = 0 has a(0) = 0 digits '2'.
1^3 = 1 has a(1) = 0 digits '2'.
2^3 = 8 has a(2) = 0 digits '2'.
3^3 = 27 has a(3) = 1 digits '2'.
4^3 = 64 has a(4) = 0 digits '2'.
5^3 = 125 has a(5) = 1 digit '2'.
28^3 = 21952 is the least cube which has a(28) = 2 digits '2'.

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A036529 and A036527 - A036536; A048367 and A048365 - A048374.
Analog for the other digits 0, 1, ..., 9: A269250, A269241, A269242, A269243, A269244, A269245, A269246, A269247, A269248, A269249.
Analog for squares: A086010 (digit 2), and A086008 - A086017 for digits 0 - 9.

[Multiplicity(Intseq(n^3),2): n in [0..100]]; // Marius A. Burtea, Jan 26 2020

seq(numboccur(2,convert(n^3,base,10)),n=0..100); # Robert Israel, Jan 26 2020

Table[DigitCount[n^3, 10, 2], {n, 0, 100}] (* Robert Price, Mar 21 2020 *)

A269242(n)=#select(t->t==2,digits(n^3))

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

A086015 Number of 7's in decimal expansion of n^2.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 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, 3's A086011, 4's A086012, 5's A086013, 6's A086014, 8's A086016, 9's A086017.

Cf. A269247 for the n^3 analog.

DigitCount[(Range[0, 100])^2, 10, 7] (* G. C. Greubel, Dec 13 2016 *)

A086015(n)=#select(d->d==7,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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A086016 Number of 8's in decimal expansion of n^2.

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A269242 Number of times the digit 2 appears in the decimal expansion of n^3.

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