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A155881
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a(n) is the number of zeros needed to write the integers 1 through Fibonacci(n).
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1
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0, 0, 0, 0, 0, 0, 1, 2, 3, 5, 8, 24, 43, 67, 121, 188, 409, 708, 1228, 1946, 4131, 6241, 10525, 17866, 29428, 58369, 87881, 156261, 255242, 412545, 767846, 1280460, 2059307, 3343656, 5510186, 9861418, 16472261, 26422596, 43917688, 73697381, 125281166, 206655249
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OFFSET
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1,8
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COMMENTS
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Data suggets a(n) ~= 10 ^ (c * n) where c ~= 0.209. - David A. Corneth, Jan 23 2019
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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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
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MATHEMATICA
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Block[{n = 32, s}, s = DigitCount[Range@ Fibonacci@ n, 10, 0]; Array[Total@ Take[s, Fibonacci@ #] &, n]] (* Michael De Vlieger, Jan 23 2019 *)
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PROG
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(PARI) nb(n) = #Set(select(x->(x==0), digits(n))); \\ A055641
a(n) = sum(k=1, fibonacci(n), nb(k)); \\ Michel Marcus, Jan 23 2019
(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 29 2009
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EXTENSIONS
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STATUS
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approved
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