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A073557 Number of Fibonacci numbers F(k), k <= 10^n, whose initial digit is 1. 1
3, 30, 301, 3011, 30103, 301031, 3010300, 30103001, 301029995, 3010299957 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..10.

FORMULA

Lim as n -> inf. 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: A136942 A136947 A093138 * 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

STATUS

approved

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Last modified June 18 18:17 EDT 2021. Contains 345120 sequences. (Running on oeis4.)