A105514 Number of times 4 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.

0, 0, 0, 0, 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, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset

0,25

Links

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

Formula

a(n) = #{k: A008963(k) = 4 and 0<=k<=n};

a(A105504(n)) = a(A105504(n) - 1) + 1;

n = A105511(n) + A105512(n) + A105513(n) + a(n) + A105515(n) + A105516(n) + A105517(n) + A105518(n) + A105519(n).

a(n) ~ log_10(5/4) * n. - Amiram Eldar, Jan 12 2023

Mathematica

Accumulate[Table[If[IntegerDigits[Fibonacci[n]][[1]] == 4, 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))==4);
(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, A105504.

Cf. A105511, A105512, A105513, A105515, A105516, A105517, A105518, A105519.

Sequence in context: A105518 A111896 A105515 * A214081 A194338 A176170

Adjacent sequences: A105511 A105512 A105513 * A105515 A105516 A105517

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2005

Status

approved