A105518 - OEIS

%I #14 Mar 18 2023 10:36:08

%S 0,0,0,0,0,0,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,

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

%U 4,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7

%N Number of times 8 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.

%H Winston de Greef, <a href="/A105518/b105518.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = #{k: A008963(k) = 8 and 0<=k<=n};

%F a(A105508(n)) = a(A105508(n) - 1) + 1;

%F n = A105511(n) + A105512(n) + A105513(n) + A105514(n) + A105515(n) + A105516(n) + A105517(n) + a(n) + A105519(n).

%F a(n) ~ log_10(9/8) * n. - _Amiram Eldar_, Jan 12 2023

%t Accumulate[Table[If[IntegerDigits[Fibonacci[n]][[1]] == 8, 1, 0], {n, 0, 100}]] (* _Amiram Eldar_, Jan 12 2023 *)

%o (PARI)

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

%o (isok(n) = leadingdigit(fibonacci(n))==8);

%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, A105508.

%Y Cf. A105511, A105512, A105513, A105514, A105515, A105516, A105517, A105519.

%K nonn,base

%O 0,12

%A _Reinhard Zumkeller_, Apr 11 2005