|
%I #18 Oct 07 2016 12:08:33
%S 6,11,30,54,73,78,97,121,140,145,164,188,207,231,255,274,298,322,341,
%T 365,389,408,432,451,456,475,499,518,523,542,566,585,590,609,633,652,
%U 676,700,719,743,767,786,810,834,853,877,896,901,920,944,963,968,987
%N Numbers m such that 8 is the leading digit of the m-th Fibonacci number in decimal representation.
%F A008963(a(n)) = A000030(A000045(a(n))) = 8.
%F A105518(a(n)) = A105518(a(n) - 1) + 1.
%F A000045(a(n)) = A045732(n).
%F a(n) ~ kn by the equidistribution theorem, where k = log(10)/(log(9) - log(8)) = 19.549378.... - _Charles R Greathouse IV_, Oct 07 2016
%e a(1)=6 since the 6th Fibonacci: 8 begins with 8.
%e a(2)=11 since the 11th Fibonacci: 89 begins with 8.
%t Flatten[Position[Fibonacci[Range[1000]],_?(First[IntegerDigits[#]]==8&)]] (* _Harvey P. Dale_, Jan 04 2015 *)
%o (PARI) isok(n) = digits(fibonacci(n))[1] == 8; \\ _Michel Marcus_, Jan 10 2014
%Y Cf. A000030, A000045, A072710, A105501, A105502, A105503, A105504, A105505, A105506, A105507, A105509.
%K nonn,base
%O 1,1
%A _Reinhard Zumkeller_, Apr 11 2005
%E Example and formulas edited by _Michel Marcus_, Jan 10 2014
|
