A073558 Number of Fibonacci numbers F(k), k <= 10^n, whose initial digit is 2.

2, 18, 177, 1762, 17610, 176092, 1760918, 17609129, 176091265, 1760912596, 17609125912

Offset

1,1

Links

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

Formula

Limit_{n->oo} a(n)/10^n = log(3/2), where the base is 10. - Robert Gerbicz, Sep 05 2002

Example

a(2) = 18 because there are 18 Fibonacci numbers up to 10^2 whose initial digit is 2.

Prog

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

Crossrefs

Sequence in context: A364524 A092473 A318218 * A132306 A264196 A214768

Adjacent sequences: A073555 A073556 A073557 * A073559 A073560 A073561

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 09 2024

Status

approved