A105511 Number of times 1 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.

0, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 7, 7, 7, 7, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 13, 13, 13, 13, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18, 19, 20, 20, 20, 20, 21, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24

Offset

0,3

Links

Winston de Greef, Table of n, a(n) for n = 0..10000

Formula

a(n) = #{k: A008963(k) = 1 and 0<=k<=n};

a(A105501(n)) = a(A105501(n) - 1) + 1;

n = a(n) + A105512(n) + A105513(n) + A105514(n) + A105515(n) + A105516(n) + A105517(n) + A105518(n) + A105519(n).

a(n) ~ log_10(2) * n. - Amiram Eldar, Jan 12 2023

Mathematica

Accumulate[Table[If[IntegerDigits[Fibonacci[n]][[1]] == 1, 1, 0], {n, 0, 100}]] (* Amiram Eldar, Jan 12 2023 *)

Prog

(PARI)
(leadingdigit(n, b=10) = n \ 10^logint(n, b));
(isok(n) = leadingdigit(fibonacci(n))==1);
(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

Crossrefs

Cf. A000030, A000045, A008963, A105501.

Cf. A105512, A105513, A105514, A105515, A105516, A105517, A105518, A105519.

Sequence in context: A075249 A008648 A154099 * A187183 A027868 A060384

Adjacent sequences: A105508 A105509 A105510 * A105512 A105513 A105514

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2005

Status

approved