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

1,1

Comments

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

Links

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A031331 A236838 A138091 * A015911 A188005 A054520

Adjacent sequences: A105504 A105505 A105506 * A105508 A105509 A105510

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2005

Status

approved