A305930 - OEIS

%I #4 Jun 23 2018 09:18:28

%S 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,

%T 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,

%U 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

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

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

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

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

%t Table[ Count[ IntegerDigits[3^n], 0], {n, 0, 100} ]

%t DigitCount[3^Range[0,110],10,0]

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

%o (Haskell) a305930 = a055641 . a000244

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

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

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

%K nonn,base

%O 0,22

%A _M. F. Hasler_, Jun 22 2018