This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A105519 #18 Mar 18 2023 11:30:43 %S A105519 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, %T A105519 1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3, %U A105519 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5 %N A105519 Number of times 9 is the leading digit of the first n+1 Fibonacci numbers in decimal representation. %H A105519 Winston de Greef, <a href="/A105519/b105519.txt">Table of n, a(n) for n = 0..10000</a> %F A105519 a(n) = #{k: A008963(k) = 9 and 0<=k<=n}; %F A105519 a(A105509(n)) = a(A105509(n) - 1) + 1; %F A105519 n = A105511(n) + A105512(n) + A105513(n) + A105514(n) + A105515(n) + A105516(n) + A105517(n) + A105518(n) + a(n). %F A105519 a(n) ~ (1 - log_10(9)) * n. - _Amiram Eldar_, Jan 12 2023 %t A105519 Table[If[First[IntegerDigits[Fibonacci[n]]]==9,1,0],{n,0,110}]// Accumulate (* _Harvey P. Dale_, Nov 27 2018 *) %o A105519 (PARI) %o A105519 (leadingdigit(n, b=10) = n \ 10^logint(n, b)); %o A105519 (isok(n) = leadingdigit(fibonacci(n))==9); %o A105519 (lista(n)=my(a=vector(1+n), r=0); for (i=1, n, r+=isok(i); a[1+i]=r); a) \\ _Winston de Greef_, Mar 18 2023 %Y A105519 Cf. A000030, A000045, A008963, A105509. %Y A105519 Cf. A105511, A105512, A105513, A105514, A105515, A105516, A105517, A105518. %K A105519 nonn,base %O A105519 0,36 %A A105519 _Reinhard Zumkeller_, Apr 11 2005