A105516 Number of times 6 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, 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, 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, 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

Offset

0,21

Links

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

Formula

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

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

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

a(n) ~ log_10(7/6) * n. - Amiram Eldar, Jan 12 2023

Mathematica

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

Prog

(PARI)
(leadingdigit(n, b=10) = n \ 10^logint(n, b));
(isok(n) = leadingdigit(fibonacci(n))==6);
(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, A105506.

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

Sequence in context: A194334 A242259 A048766 * A105518 A111896 A105515

Adjacent sequences: A105513 A105514 A105515 * A105517 A105518 A105519

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2005

Status

approved