A073560 Number of Fibonacci numbers F(k), k <= 10^n, whose initial digit is 4.

0, 9, 96, 968, 9690, 96908, 969101, 9690998, 96910014, 969100129, 9691001297

Offset

1,2

Links

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

Formula

Limit_{n->oo} a(n)/10^n = log(5/4), where the base is 10. - Robert Gerbicz, Sep 05 2002

Example

a(2) = 9 because there are 9 Fibonacci numbers up to 10^2 whose initial digit is 4.

Prog

(PARI) lista(nn) = my(m=log(quadgen(5)), c=-1, d=log(10)/m, q, r=log(sqrt(5))/m, s=3-log(4)/m, t=4-log(5)/m, u=1); for(n=1, nn, u=10*u; until(u<r+=d, q=frac(r); if(q<s || q>t, c++)); print1(c - (q<s&&r-d+2>u || q>t&&r-d+3>u), ", ")); \\ Jinyuan Wang, Dec 09 2024

Crossrefs

Sequence in context: A264219 A005545 A228007 * A069055 A228011 A024116

Adjacent sequences: A073557 A073558 A073559 * A073561 A073562 A073563

Keyword

nonn,base,more

Author

Shyam Sunder Gupta, Aug 15 2002

Extensions

More terms from Robert Gerbicz, Sep 05 2002

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

Status

approved