A105508 Numbers m such that 8 is the leading digit of the m-th Fibonacci number in decimal representation.

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

Links

Table of n, a(n) for n=1..53.

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

Crossrefs

Cf. A000030, A000045, A072710, A105501, A105502, A105503, A105504, A105505, A105506, A105507, A105509.

Sequence in context: A034489 A231410 A285917 * A114960 A320482 A151790

Adjacent sequences: A105505 A105506 A105507 * A105509 A105510 A105511

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2005

Extensions

Example and formulas edited by Michel Marcus, Jan 10 2014

Status

approved