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A072353
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a(n) is the index of the largest Fibonacci number containing n digits.
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7
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6, 11, 16, 20, 25, 30, 35, 39, 44, 49, 54, 59, 63, 68, 73, 78, 83, 87, 92, 97, 102, 106, 111, 116, 121, 126, 130, 135, 140, 145, 150, 154, 159, 164, 169, 173, 178, 183, 188, 193, 197, 202, 207, 212, 216, 221, 226, 231, 236, 240, 245, 250, 255, 260, 264, 269, 274
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Lim_{n->infinity} a(n)/n = 1/log_10((1+sqrt(5))/2) = 4.784... . - Reinhard Zumkeller, Apr 14 2005
Equivalently, a(n) is the number of Fibonacci numbers < 10^n including F(0) = 0 and F(1) = F(2) = 1 once. - Derek Orr, Jun 01 2014
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LINKS
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EXAMPLE
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a(3)=16, as the 16th Fibonacci number is the largest Fibonacci number with 3 digits.
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MATHEMATICA
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With[{fibs=Fibonacci[Range[300]]}, Flatten[Position[fibs, #]&/@ Table[ Max[ Select[fibs, IntegerLength[#]==n&]], {n, 60}]]] (* Harvey P. Dale, Nov 09 2011 *)
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PROG
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(Python)
list = []
x, y, index = 1, 1, 1
while len(list) < n:
if len(str(x)) < len(str(y)):
list.append(index)
x, y = y, x + y
index += 1
return list
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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