A240962 Number of zeros in the decimal expansion of n^n.

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

Offset: 1

Author

Anthony Sand, Aug 05 2014

Keywords

• nonn
• base

Examples

			a(1) = zerocount(1^1) = zerocount(1) = 0.
a(8) = zerocount(8^8) = zerocount(16777216) = 0.
a(9) = zerocount(9^9) = zerocount(387420489) = 1.
a(10) = zerocount(10^10) = zerocount(10000000000) = 10.
		

Links

• Anthony Sand, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Maple

seq(numboccur(0,convert(n^n,base,10)), n=1 .. 100); # Robert Israel, Aug 05 2014

Mathematica

Map[Count[IntegerDigits[#^#], 0] &, Range[2, 100]] (* Michael De Vlieger, Aug 06 2014 *)

PARI

a(n) = my(d = digits(n^n)); sum(i=1, #d, ! d[i]); \\ Michel Marcus, Aug 10 2014

Python

for n in range(1,10**3):
  print(str(n**n).count('0'),end=', ') # Derek Orr, Aug 05 2014

Formula

a(n) = A055641(A000312(n)). - Michel Marcus, Aug 07 2014