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%I #32 Jan 23 2019 10:30:16
%S 0,0,0,0,0,0,1,2,3,5,8,24,43,67,121,188,409,708,1228,1946,4131,6241,
%T 10525,17866,29428,58369,87881,156261,255242,412545,767846,1280460,
%U 2059307,3343656,5510186,9861418,16472261,26422596,43917688,73697381,125281166,206655249
%N a(n) is the number of zeros needed to write the integers 1 through Fibonacci(n).
%C Data suggets a(n) ~= 10 ^ (c * n) where c ~= 0.209. - _David A. Corneth_, Jan 23 2019
%H David A. Corneth, <a href="/A155881/b155881.txt">Table of n, a(n) for n = 1..4770</a>
%F a(n) = A061217(Fibonacci(n)) = A061217(A000045(n)). - _David A. Corneth_, Jan 23 2019
%e F(9)=34, so writing the numbers F(1)..F(9) requires 3 zeros (one each at 10, 20, and 30), thus a(9)=3.
%p A055641 := proc(n) option remember ; local a,d; if n = 0 then RETURN(a) ; fi; a := 0 ; for d in convert(n,base,10) do if d = 0 then a := a+1 ; fi; od: a ; end: A155881 := proc(n) add(A055641(i),i=1..combinat[fibonacci](n)) ; end: for n from 1 do printf("%d,\n",A155881(n)) ; od; # _R. J. Mathar_, Feb 19 2009
%t Block[{n = 32, s}, s = DigitCount[Range@ Fibonacci@ n, 10, 0]; Array[Total@ Take[s, Fibonacci@ #] &, n]] (* _Michael De Vlieger_, Jan 23 2019 *)
%o (PARI) nb(n) = #Set(select(x->(x==0), digits(n))); \\ A055641
%o a(n) = sum(k=1, fibonacci(n), nb(k)); \\ _Michel Marcus_, Jan 23 2019
%o (PARI) a(n) = my(n = fibonacci(n), m=logint(n, 10)); (m+1)*(n+1) - (10^(m+1)-1)/9 + (1/2) * sum(j=1, m+1, (n\10^j * (2*n+2 - (1 + n\10^j) * 10 ^ j) - floor(n/10^j+9/10) * (2*n+2 + ((4/5 - floor(n / 10^j + 9 / 10))*10^j)))) \\ _David A. Corneth_, Jan 23 2019
%Y Cf. A000045, A055641, A061217.
%K nonn,base
%O 1,8
%A Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 29 2009
%E 8 more terms from _R. J. Mathar_, Feb 19 2009
%E 9 more terms from _Sean A. Irvine_, Dec 10 2009
%E Edited by _Jon E. Schoenfield_, Jan 22 2019
%E More terms from _David A. Corneth_, Jan 23 2019
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