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

Author

Reinhard Zumkeller, Apr 11 2005

Keywords

• nonn
• base

Examples

			a(1)=6 since the 6th Fibonacci: 8 begins with 8.
a(2)=11 since the 11th Fibonacci: 89 begins with 8.
		

Crossrefs

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

Programs

Mathematica

Flatten[Position[Fibonacci[Range[1000]],?(First[IntegerDigits[#]]==8&)]] (* _Harvey P. Dale, Jan 04 2015  *)

PARI

isok(n) = digits(fibonacci(n))[1] == 8; \\ Michel Marcus, Jan 10 2014

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

Extensions

Example and formulas edited by Michel Marcus, Jan 10 2014