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A105509
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Numbers m such that 9 is the leading digit of the m-th Fibonacci number in decimal representation.
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9
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16, 35, 59, 83, 102, 126, 150, 169, 193, 212, 236, 260, 279, 303, 327, 346, 370, 394, 413, 437, 461, 480, 504, 528, 547, 571, 595, 614, 638, 657, 681, 705, 724, 748, 772, 791, 815, 839, 858, 882, 906, 925, 949, 973, 992, 1016, 1040, 1059, 1083, 1102, 1107
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OFFSET
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1,1
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COMMENTS
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Comment from Jonathan Vos Post, Dec 23 2006: Peterson says: "Calculate 100/89 = 1.1235955056... This fraction generates the first five Fibonacci numbers before blurring into other digits. ... 10000/9899 = 1.0102030508132134559046368... generates the first 10 Fibonacci numbers (using two digits per number). 1000000/998999 generates the first 15 Fibonacci numbers (using three digits per number). ... in successive fractions, two 0's are appended to the numerator and a 9 to the beginning and end of the denominator...."
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LINKS
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Ivars Peterson, Designer Decimals, Science News, Week of Nov 04 2006; Vol. 170, No. 19.
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FORMULA
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m such that d(m+5)-d(m) = 2 for d(m) = floor(1 + log_10(F(m))) and F(m) = m-th Fibonacci number = A000045(m). - Jonathan Vos Post, Dec 23 2006
a(n) ~ k*n by the equidistribution theorem, where k = 1/(1 - log(9)/log(10)) = 21.8543.... - Charles R Greathouse IV, Oct 07 2016
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EXAMPLE
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A000030(90343046356137747723758225621187571439538669) = 9.
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MATHEMATICA
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Select[Range@ 1200, First@ IntegerDigits@ Fibonacci@ # == 9 &] (* Michael De Vlieger, Aug 21 2016 *)
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PROG
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CROSSREFS
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Cf. A000030, A000045, A072711, A105501, A105502, A105503, A105504, A105505, A105506, A105507, A105508.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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