A055641 Number of zero digits in n.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 1, 1

Offset

0,101

Links

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Formula

From Hieronymus Fischer, Jun 06 2012: (Start)

a(n) = m + 1 - A055640(n) = Sum_{j=1..m+1} (1 + floor(n/10^j) - floor(n/10^j+0.9)), where m = floor(log_10(n)).

G.f.: g(x) = 1 + (1/(1-x))*Sum_{j>=0} (x^(10*10^j) - x^(11*10^j))/(1-x^10^(j+1)). (End)

a(n) = if n<10 then A000007(n) else a(A059995(n)) + A000007(A010879(n)). - Reinhard Zumkeller, Apr 30 2013, corrected by M. F. Hasler, Jun 22 2018

Example

a(99) = 0 because the digits of 99 are 9 and 9, a(100) = 2 because the digits of 100 are 1, 0 and 0 and there are two 0's.

Mathematica

Array[Last@ DigitCount@ # &, 105] (* Michael De Vlieger, Jul 02 2015 *)

Prog

(Haskell)
a055641 n | n < 10    = 0 ^ n
          | otherwise = a055641 n' + 0 ^ d where (n', d) = divMod n 10
-- Reinhard Zumkeller, Apr 30 2013
(PARI) a(n)=if(n, n=digits(n); sum(i=2, #n, n[i]==0), 1) \\ Charles R Greathouse IV, Sep 13 2015
(PARI) A055641(n)=#select(d->!d, digits(n))+!n \\ M. F. Hasler, Jun 22 2018
(Python)
def a(n): return str(n).count("0")
print([a(n) for n in range(106)]) # Michael S. Branicky, May 26 2022

Crossrefs

Cf. A011540, A004719, A052382, A054899, A055640, A102669-A102685, A122840, A160093, A160094, A196563, A195564, A000120, A000788, A023416, A059015 (for base 2), A085974.

Sequence in context: A029419 A165105 A325674 * A218245 A352516 A086075

Adjacent sequences: A055638 A055639 A055640 * A055642 A055643 A055644

Keyword

base,easy,nonn

Author

Henry Bottomley, Jun 06 2000

Status

approved