login
A105502
Numbers m such that 2 is the leading digit of the m-th Fibonacci number in decimal representation.
10
3, 8, 13, 18, 23, 32, 37, 42, 47, 51, 56, 61, 66, 75, 80, 85, 90, 99, 104, 109, 114, 118, 123, 128, 133, 142, 147, 152, 157, 166, 171, 176, 185, 190, 195, 200, 209, 214, 219, 224, 233, 238, 243, 252, 257, 262, 267, 276, 281, 286, 291, 295, 300, 305, 310, 319
OFFSET
1,1
COMMENTS
A008963(a(n)) = 2; A105512(a(n)) = A105512(a(n) - 1) + 1.
LINKS
FORMULA
a(n) ~ kn by the equidistribution theorem, where k = log(10)/(log(3) - log(2)) = 5.67887.... - Charles R Greathouse IV, Oct 07 2016
EXAMPLE
a(10)=51: A008963(51) = A000030(A000045(51)) = A000030(20365011074) = 2.
MATHEMATICA
Select[Range[400], First[IntegerDigits[Fibonacci[#]]]==2&] (* Harvey P. Dale, Jul 13 2015 *)
PROG
(PARI) is(n)=digits(fibonacci(n))[1]==2 \\ Charles R Greathouse IV, Oct 07 2016
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 11 2005
STATUS
approved