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A105508
Numbers m such that 8 is the leading digit of the m-th Fibonacci number in decimal representation.
9
6, 11, 30, 54, 73, 78, 97, 121, 140, 145, 164, 188, 207, 231, 255, 274, 298, 322, 341, 365, 389, 408, 432, 451, 456, 475, 499, 518, 523, 542, 566, 585, 590, 609, 633, 652, 676, 700, 719, 743, 767, 786, 810, 834, 853, 877, 896, 901, 920, 944, 963, 968, 987
OFFSET
1,1
FORMULA
A008963(a(n)) = A000030(A000045(a(n))) = 8.
A105518(a(n)) = A105518(a(n) - 1) + 1.
A000045(a(n)) = A045732(n).
a(n) ~ kn by the equidistribution theorem, where k = log(10)/(log(9) - log(8)) = 19.549378.... - Charles R Greathouse IV, Oct 07 2016
EXAMPLE
a(1)=6 since the 6th Fibonacci: 8 begins with 8.
a(2)=11 since the 11th Fibonacci: 89 begins with 8.
MATHEMATICA
Flatten[Position[Fibonacci[Range[1000]], _?(First[IntegerDigits[#]]==8&)]] (* Harvey P. Dale, Jan 04 2015 *)
PROG
(PARI) isok(n) = digits(fibonacci(n))[1] == 8; \\ Michel Marcus, Jan 10 2014
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 11 2005
EXTENSIONS
Example and formulas edited by Michel Marcus, Jan 10 2014
STATUS
approved