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A055641 Number of zero digits in n. 50
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,101

LINKS

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

FORMULA

Contribution from Hieronymus Fischer, Jun 06 2012 (Start):

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

a(n) = m + 1 - A055640(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 A059995(n) + A000007(A010879(n)). - Reinhard Zumkeller, Apr 30 2013

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

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: A212627 A029419 A165105 * A218245 A086075 A056978

Adjacent sequences:  A055638 A055639 A055640 * A055642 A055643 A055644

KEYWORD

base,easy,nonn

AUTHOR

Henry Bottomley, Jun 06 2000

STATUS

approved

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Last modified June 21 23:16 EDT 2018. Contains 305646 sequences. (Running on oeis4.)