A073563 Number of Fibonacci numbers F(k), k <= 10^n, whose initial digit is 7.

0, 5, 56, 580, 5798, 57992, 579913, 5799197, 57991941, 579919465, 5799194699

Offset

1,2

Links

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

Formula

Limit_{n->oo} a(n)/10^n = log(8/7), where the base is 10. - Robert Gerbicz, Sep 05 2002

Example

a(2) = 5 because there are 5 Fibonacci numbers up to 10^2 whose initial digit is 7.

Prog

(PARI) lista(nn) = my(m=log(quadgen(5)), c=0, d=log(10)/m, q, r=log(sqrt(5))/m, s=5-log(7)/m, t=5-log(8)/m, 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: A258490 A255953 A174249 * A006658 A221160 A006293

Adjacent sequences: A073560 A073561 A073562 * A073564 A073565 A073566

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