A105507 Numbers m such that 7 is the leading digit of the n-th Fibonacci number in decimal representation.

25, 44, 49, 68, 92, 111, 116, 135, 159, 178, 183, 202, 226, 245, 250, 269, 293, 312, 317, 336, 360, 379, 384, 403, 427, 446, 470, 489, 494, 513, 537, 556, 561, 580, 604, 623, 628, 647, 671, 690, 695, 714, 738, 757, 762, 781, 805, 824, 829, 848, 872, 891, 915

Offset: 1

Author

Reinhard Zumkeller, Apr 11 2005

Keywords

• nonn
• base

Comments

A008963(a(n)) = 7; A105517(a(n)) = A105517(a(n) - 1) + 1.

Examples

			a(10)=178: A008963(178) = A000030(A000045(178)) =
A000030(7084593923980518516849609894969925639) = 7.
		

Crossrefs

Cf. A000030, A000045, A072709, A105501, A105502, A105503, A105504, A105505, A105506, A105508, A105509.

Programs

Mathematica

Flatten[Position[Fibonacci[Range[1000]],?(IntegerDigits[#][[1]]==7&)]] (* _Harvey P. Dale, Nov 20 2015 *)

PARI

is(n)=digits(fibonacci(n))[1]==7 \\ Charles R Greathouse IV, Oct 07 2016

Formula

a(n) ~ kn by the equidistribution theorem, where k = log(10)/(log(8) - log(7)) = 17.24377.... - Charles R Greathouse IV, Oct 07 2016