A269250 Number of times the digit 0 appears in the decimal expansion of n^3.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 1, 0, 0, 3, 0, 1, 1, 0, 0, 0, 1, 1, 0, 3, 0, 2, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 2, 0, 0, 0, 2, 0, 1, 3, 0, 0, 1, 1, 0, 0, 0, 0, 1, 3, 0, 0, 0, 1, 0, 1, 1, 0, 1, 3, 0, 0, 1, 1, 0, 0, 0, 0, 1, 6

Offset: 0

Author

M. F. Hasler, Feb 20 2016

Keywords

• nonn
• base

Comments

The cubes corresponding to the first occurrence of 1, 2, 3, ... are listed in A036527, i.e., A048365(n) = A036527(n)^(1/3) is the index of the first occurrence of n.

Examples

			1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, ..., 9^3 = 729 all have a(1) = a(2) = ... = a(9) = 0 digits '0'.
0^3 = 0 has a(0) = 1 digit '0'.
10^3 = 1000 has a(10) = 3 digits '0'.
		

Links

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

Crossrefs

Cf. A048365 = A036527^(1/3); A036528 - A036536 and A048366 - A048374.

Analog for the other digits 1, ..., 9: A269241, A269242, A269243, A269244, A269245, A269246, A269247, A269248, A269249.

Analog for squares: A086008 (digit 0), and A086009 - A086017 for digits 1 - 9.

Programs

Maple

seq(numboccur(0, convert(n^3,base,10)), n=0..100); # Robert Israel, Feb 21 2016

Mathematica

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

PARI

A269250(n)=!n+#select(t->!t,digits(n^3))