A305930 Number of digits '0' in 3^n (in base 10).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 3, 2, 0, 0, 1, 0, 0, 0, 1, 2, 0, 2, 2, 0, 4, 2, 3, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 3, 1, 2, 1, 2, 7, 6, 2, 5, 2, 4, 2, 2, 2, 1, 2, 4, 4, 3, 0, 2, 4, 2, 1, 1, 4, 3, 5, 4, 5, 4, 5, 3, 3, 2, 6, 6, 5, 3, 4, 5, 3, 5, 5, 2, 6, 6, 2, 6, 4, 7

Offset: 0

Author

M. F. Hasler, Jun 22 2018

Keywords

• nonn
• base

Examples

			3^10 = 59049 is the smallest power of 3 having a digit 0, so a(10) = 1 is the first nonzero term.
		

Crossrefs

Cf. A027870 (analog for 2^k), A030700 (indices of zeros).

Cf. A063555: index of first appearence of n in this sequence.

Cf. A305933: table with n in row a(n).

Programs

Haskell

a305930 = a055641 . a000244

Mathematica

Table[ Count[ IntegerDigits[3^n], 0], {n, 0, 100} ]
DigitCount[3^Range[0,110],10,0]

PARI

apply( A305930(n)=#select(d->!d,digits(3^n)), [0..99])

Formula

a(n) = A055641(A000244(n)).

a(A030700(n)) = 0; a(A305934(n)) = 1; a(A305931(n)) >= 1; a(A305933(n,k)) = n.