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Number of times the digit 0 appears in the decimal expansion of n^3.
14

%I #26 Mar 21 2020 16:34:21

%S 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,

%T 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,

%U 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

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

%C 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.

%H Robert Israel, <a href="/A269250/b269250.txt">Table of n, a(n) for n = 0..10000</a>

%e 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'.

%e 0^3 = 0 has a(0) = 1 digit '0'.

%e 10^3 = 1000 has a(10) = 3 digits '0'.

%p seq(numboccur(0, convert(n^3,base,10)), n=0..100); # _Robert Israel_, Feb 21 2016

%t Table[DigitCount[n^3, 10, 0], {n, 0, 100}] (* _Robert Price_, Mar 21 2020 *)

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

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

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

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

%K nonn,base

%O 0,11

%A _M. F. Hasler_, Feb 20 2016