A105507 - OEIS

%I #7 Oct 07 2016 12:06:55

%S 25,44,49,68,92,111,116,135,159,178,183,202,226,245,250,269,293,312,

%T 317,336,360,379,384,403,427,446,470,489,494,513,537,556,561,580,604,

%U 623,628,647,671,690,695,714,738,757,762,781,805,824,829,848,872,891,915

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

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

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

%e a(10)=178: A008963(178) = A000030(A000045(178)) =

%e A000030(7084593923980518516849609894969925639) = 7.

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

%o (PARI) is(n)=digits(fibonacci(n))[1]==7 \\ _Charles R Greathouse IV_, Oct 07 2016

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

%K nonn,base

%O 1,1

%A _Reinhard Zumkeller_, Apr 11 2005