A073565 Number of Fibonacci numbers F(k), k <= 10^n, whose initial digit is 9.

0, 4, 45, 456, 4575, 45758, 457571, 4575752, 45757486, 457574900, 4575749050

Offset

1,2

Links

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

Formula

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

Example

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

Prog

(PARI) lista(nn) = my(m=log(quadgen(5)), c=0, d=log(10)/m, q, r=log(sqrt(5))/m, s=5-log(9)/m, t=5-d, 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: A232729 A055602 A346629 * A039657 A114473 A275125

Adjacent sequences: A073562 A073563 A073564 * A073566 A073567 A073568

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