A105502 Numbers m such that 2 is the leading digit of the m-th Fibonacci number in decimal representation.

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

Author

Reinhard Zumkeller, Apr 11 2005

Keywords

• nonn
• base

Comments

A008963(a(n)) = 2; A105512(a(n)) = A105512(a(n) - 1) + 1.

Examples

			a(10)=51: A008963(51) = A000030(A000045(51)) = A000030(20365011074) = 2.
		

Links

• Winston de Greef, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000030, A000045, A072682, A105501, A105503, A105504, A105505, A105506, A105507, A105508, A105509.

Programs

Mathematica

Select[Range[400],First[IntegerDigits[Fibonacci[#]]]==2&] (* Harvey P. Dale, Jul 13 2015 *)

PARI

is(n)=digits(fibonacci(n))[1]==2 \\ Charles R Greathouse IV, Oct 07 2016

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