A073564 Number of Fibonacci numbers F(k), k <= 10^n, whose initial digit is 8.

1, 7, 53, 513, 5117, 51151, 511531, 5115248, 51152529, 511525232, 5115252247

Offset

1,2

Links

Table of n, a(n) for n=1..11.

Formula

Limit_{n->oo} a(n)/10^n = log(9/8), where the base is 10. - Robert Gerbicz, Sep 05 2002

Example

a(2) = 7 because there are 7 Fibonacci numbers F(k), k <= 10^2 whose initial digit is 8, namely:
  k  F(k)
  6  8
  11 89
  30 832040
  54 86267571272
  73 806515533049393
  78 8944394323791464
  97 83621143489848422977

Mathematica

Table[Count[Fibonacci[Range[10^n]], _?(IntegerDigits[#][[1]]==8&)], {n, 1, 5}] (* Harvey P. Dale, Feb 26 2023 *)

Prog

(PARI) lista(nn) = my(m=log(quadgen(5)), c=0, d=log(10)/m, q, r=log(sqrt(5))/m, s=5-log(8)/m, t=5-log(9)/m, u=-3); for(n=1, nn, u=10*u+36; until(u<r+=d, q=frac(r); if(q<s && q>t, c++)); print1(c, ", ")); \\ Jinyuan Wang, Dec 09 2024

Crossrefs

Sequence in context: A137612 A092802 A062207 * A372939 A194929 A317689

Adjacent sequences: A073561 A073562 A073563 * A073565 A073566 A073567

Keyword

nonn,base,more

Author

Shyam Sunder Gupta, Aug 15 2002

Extensions

Corrected and extended by Robert Gerbicz, Sep 05 2002

Data corrected by Harvey P. Dale_, Feb 25 2023 [The terms were off by 1]

Edited by N. J. A. Sloane, Feb 25 2023

a(9)-a(11) from Sean A. Irvine and Jinyuan Wang, Dec 10 2024

a(0) removed by Sean A. Irvine, Dec 10 2024

Status

approved