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Number of zeros in the decimal expansion of n^n.
2

%I #30 Aug 21 2014 22:55:08

%S 0,0,0,0,0,0,0,0,1,10,1,2,2,3,2,2,1,2,1,21,1,0,5,2,3,6,3,1,1,32,6,5,7,

%T 7,3,3,6,8,6,42,5,6,10,10,5,11,4,12,11,53,5,6,12,10,8,11,15,9,5,64,12,

%U 15,14,16,13,12,13,9,16,79,12,16,15,12,14,15

%N Number of zeros in the decimal expansion of n^n.

%H Anthony Sand, <a href="/A240962/b240962.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A055641(A000312(n)). - _Michel Marcus_, Aug 07 2014

%e a(1) = zerocount(1^1) = zerocount(1) = 0.

%e a(8) = zerocount(8^8) = zerocount(16777216) = 0.

%e a(9) = zerocount(9^9) = zerocount(387420489) = 1.

%e a(10) = zerocount(10^10) = zerocount(10000000000) = 10.

%p seq(numboccur(0,convert(n^n,base,10)), n=1 .. 100); # _Robert Israel_, Aug 05 2014

%t Map[Count[IntegerDigits[#^#], 0] &, Range[2, 100]] (* _Michael De Vlieger_, Aug 06 2014 *)

%o (Python)

%o for n in range(1,10**3):

%o ..print(str(n**n).count('0'),end=', ') # _Derek Orr_, Aug 05 2014

%o (PARI) a(n) = my(d = digits(n^n)); sum(i=1, #d, ! d[i]); \\ _Michel Marcus_, Aug 10 2014

%Y Cf. A000312, A055641, A027870, A066588, A240963.

%K nonn,base

%O 1,10

%A _Anthony Sand_, Aug 05 2014