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A105512 Number of times 2 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.

%I A105512 #26 Mar 18 2023 11:22:01
%S A105512 0,0,0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,6,6,
%T A105512 6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,10,10,11,11,11,11,11,12,
%U A105512 12,12,12,12,13,13,13,13,13,13,13,13,13,14,14,14,14,14,15,15,15,15,15,16,16
%N A105512 Number of times 2 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.
%H A105512 Winston de Greef, <a href="/A105512/b105512.txt">Table of n, a(n) for n = 0..10000</a>
%F A105512 a(n) = #{k: A008963(k) = 2 and 0<=k<=n};
%F A105512 a(A105502(n)) = a(A105502(n) - 1) + 1;
%F A105512 n = A105511(n) + a(n) + A105513(n) + A105514(n) + A105515(n) + A105516(n) + A105517(n) + A105518(n) + A105519(n).
%F A105512 a(n) ~ log_10(3/2) * n. - _Amiram Eldar_, Jan 12 2023
%t A105512 Accumulate[Table[If[IntegerDigits[Fibonacci[n]][[1]] == 2, 1, 0], {n, 0, 100}]] (* _Amiram Eldar_, Jan 12 2023 *)
%o A105512 (PARI)
%o A105512 (leadingdigit(n, b=10) = n \ 10^logint(n, b));
%o A105512 (isok(n) = leadingdigit(fibonacci(n))==2);
%o A105512 (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 A105512 Cf. A000030, A000045, A008963, A105502.
%Y A105512 Cf. A105511, A105513, A105514, A105515, A105516, A105517, A105518, A105519.
%K A105512 nonn,base
%O A105512 0,9
%A A105512 _Reinhard Zumkeller_, Apr 11 2005