A073561 Number of Fibonacci numbers F(k), k <= 10^n, whose initial digit is 5.

2, 8, 80, 792, 7918, 79182, 791817, 7918132, 79181254, 791812468, 7918124617

Offset

1,1

Links

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

Formula

Limit_{n->oo} a(n)/10^n = log(6/5), where the base is 10. - Robert Gerbicz, Sep 05 2002

Example

a(2) = 8 because there are 8 Fibonacci numbers up to 10^2 whose initial digit is 5.

Prog

(PARI) lista(nn) = my(m=log(quadgen(5)), c=1, d=log(10)/m, q, r=log(sqrt(5))/m, s=4-log(5)/m, t=4-log(6)/m, u=-2); for(n=1, nn, u=10*u+27; until(u<r+=d, q=frac(r); if(q<s && q>t, c++)); print1(c, ", ")); \\ Jinyuan Wang, Dec 09 2024

Crossrefs

Sequence in context: A071254 A063528 A259705 * A258970 A230880 A361425

Adjacent sequences: A073558 A073559 A073560 * A073562 A073563 A073564

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