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
KEYWORD
base,easy,nonn
AUTHOR
Henry Bottomley, Jun 06 2000
STATUS
approved