A269249 Number of times the digit 9 appears in the decimal expansion of n^3.

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

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 A036535, i.e., A036535(n)^(1/3) = A048374(n) is the index of the first occurrence of n.

Examples

			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'.
		

Links

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

Crossrefs

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.

Programs

Mathematica

DigitCount[(Range[0, 100])^3, 10, 9] (* G. C. Greubel, Dec 13 2016 *)

PARI

A269249(n)=#select(t->t==9,digits(n^3))