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A105501
Numbers n such that 1 is the leading digit of the n-th Fibonacci number in decimal representation.
11
1, 2, 7, 12, 17, 21, 22, 26, 27, 31, 36, 40, 41, 45, 46, 50, 55, 60, 64, 65, 69, 70, 74, 79, 84, 88, 89, 93, 94, 98, 103, 107, 108, 112, 113, 117, 122, 127, 131, 132, 136, 137, 141, 146, 151, 155, 156, 160, 161, 165, 170, 174, 175, 179, 180, 184, 189, 194, 198, 199
OFFSET
1,2
COMMENTS
A008963(a(n)) = 1; A105511(a(n)) = A105511(a(n) - 1) + 1.
LINKS
FORMULA
a(n) ~ kn by the equidistribution theorem, where k = log(10)/log(2) = 3.321928.... - Charles R Greathouse IV, Oct 07 2016
EXAMPLE
a(10)=31: A008963(31) = A000030(A000045(31)) =
A000030(1346269) = 1.
MAPLE
filter:= proc(n) local t;
t:= combinat:-fibonacci(n);
t < 2*10^ilog10(t)
end proc:
select(filter, [$1..200]); # Robert Israel, May 02 2018
MATHEMATICA
fQ[n_] := IntegerDigits[Fibonacci[n]][[1]] == 1; Select[Range@200, fQ] (* Robert G. Wilson v, May 02 2018 *)
PROG
(PARI) is(n)=digits(fibonacci(n))[1]==1 \\ Charles R Greathouse IV, Oct 07 2016
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 11 2005
STATUS
approved