A073557 Number of Fibonacci numbers F(k), k <= 10^n, whose initial digit is 1.

3, 30, 301, 3011, 30103, 301031, 3010300, 30103001, 301029995, 3010299957, 30102999568

Offset

1,1

Links

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

Formula

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

Example

a(2) = 30 because there are 30 Fibonacci numbers up to 10^2 whose initial digit is 1.

Prog

(PARI) default(realprecision, 10^4); m=log((1+sqrt(5))/2);
lista(nn) = {my(d=log(10)/m, r=log(sqrt(5))/m, s=log(5-sqrt(5))/m, t=0, u=1); for(n=1, nn, u=10*u; while(s<u, if(floor(r+=d)==floor(s+=d), t++, t+=2)); print1(t+(r<u||floor(r)==floor(s)), ", ")); } \\ Jinyuan Wang, Feb 21 2020

Crossrefs

Cf. A000045, A047855 (numbers of integers <= 10^n, whose initial digit is 1).

Sequence in context: A136947 A093138 A361896 * A037764 A037652 A037771

Adjacent sequences: A073554 A073555 A073556 * A073558 A073559 A073560

Keyword

nonn,base,more

Author

Shyam Sunder Gupta, Aug 15 2002

Extensions

More terms from Robert Gerbicz, Sep 05 2002

a(9)-a(10) from Jinyuan Wang, Feb 21 2020

a(11) from Sean A. Irvine, Dec 04 2024

Status

approved