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A105515 Number of times 5 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.

%I A105515 #18 Mar 18 2023 11:31:16
%S A105515 0,0,0,0,0,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,
%T A105515 4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,
%U A105515 6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9
%N A105515 Number of times 5 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.
%H A105515 Winston de Greef, <a href="/A105515/b105515.txt">Table of n, a(n) for n = 0..10000</a>
%F A105515 a(n) = #{k: A008963(k) = 5 and 0<=k<=n};
%F A105515 a(A105505(n)) = a(A105505(n) - 1) + 1;
%F A105515 n = A105511(n) + A105512(n) + A105513(n) + A105514(n) + a(n) + A105516(n) + A105517(n) + A105518(n) + A105519(n).
%F A105515 a(n) ~ log_10(6/5) * n. - _Amiram Eldar_, Jan 12 2023
%t A105515 Accumulate[If[First[IntegerDigits[#]]==5,1,0]&/@Fibonacci[Range[0,110]]] (* _Harvey P. Dale_, Nov 02 2014 *)
%o A105515 (PARI)
%o A105515 (leadingdigit(n, b=10) = n \ 10^logint(n, b));
%o A105515 (isok(n) = leadingdigit(fibonacci(n))==5);
%o A105515 (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 17 2023
%Y A105515 Cf. A000030, A000045, A008963, A105505.
%Y A105515 Cf. A105511, A105512, A105513, A105514, A105516, A105517, A105518, A105519.
%K A105515 nonn,base
%O A105515 0,11
%A A105515 _Reinhard Zumkeller_, Apr 11 2005