A105516 - OEIS

%I #29 Sep 01 2024 20:00:09

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,

%T 2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,

%U 4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6

%N Number of times 6 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.

%H Winston de Greef, <a href="/A105516/b105516.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = #{k: A008963(k) = 6 and 0<=k<=n};

%F a(A105506(n)) = a(A105506(n) - 1) + 1;

%F n = A105511(n) + A105512(n) + A105513(n) + A105514(n) + A105515(n) + a(n) + A105517(n) + A105518(n) + A105519(n).

%F a(n) ~ log_10(7/6) * n. - _Amiram Eldar_, Jan 12 2023

%t Prepend[Accumulate[If[First[IntegerDigits[#]]==6,1,0]&/@Fibonacci[ Range[ 110]]],0] (* _Harvey P. Dale_, Feb 18 2011 *)

%o (PARI)

%o (leadingdigit(n, b=10) = n \ 10^logint(n, b));

%o (isok(n) = leadingdigit(fibonacci(n))==6);

%o (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 Cf. A000030, A000045, A008963, A105506.

%Y Cf. A105511, A105512, A105513, A105514, A105515, A105517, A105518, A105519.

%K nonn,base

%O 0,21

%A _Reinhard Zumkeller_, Apr 11 2005