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

Author

Shyam Sunder Gupta, Aug 15 2002

Keywords

• nonn
• base
• more

Examples

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

Programs

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(ut, c++)); print1(c, ", ")); \\ Jinyuan Wang, Dec 09 2024

Formula

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

Extensions

More terms from Robert Gerbicz, Sep 05 2002

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