A073560 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A073560

Number of Fibonacci numbers F(k), k <= 10^n, whose initial digit is 4.

0, 9, 96, 968, 9690, 96908, 969101, 9690998, 96910014, 969100129, 9691001297

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

FORMULA

Limit_{n->oo} a(n)/10^n = log(5/4), where the base is 10. - Robert Gerbicz, Sep 05 2002

EXAMPLE

a(2) = 9 because there are 9 Fibonacci numbers up to 10^2 whose initial digit is 4.

PROG

(PARI) lista(nn) = my(m=log(quadgen(5)), c=-1, d=log(10)/m, q, r=log(sqrt(5))/m, s=3-log(4)/m, t=4-log(5)/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+2>u || q>t&&r-d+3>u), ", ")); \\ Jinyuan Wang, Dec 09 2024

CROSSREFS

Sequence in context: A264219 A005545 A228007 * A069055 A228011 A024116

Adjacent sequences: A073557 A073558 A073559 * A073561 A073562 A073563

KEYWORD

nonn,base,more,changed

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