A105515 Number of times 5 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.

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, 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, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9

Offset

0,11

Links

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

Formula

a(n) = #{k: A008963(k) = 5 and 0<=k<=n};

a(A105505(n)) = a(A105505(n) - 1) + 1;

n = A105511(n) + A105512(n) + A105513(n) + A105514(n) + a(n) + A105516(n) + A105517(n) + A105518(n) + A105519(n).

a(n) ~ log_10(6/5) * n. - Amiram Eldar, Jan 12 2023

Mathematica

Accumulate[If[First[IntegerDigits[#]]==5, 1, 0]&/@Fibonacci[Range[0, 110]]] (* Harvey P. Dale, Nov 02 2014 *)

Prog

(PARI)
(leadingdigit(n, b=10) = n \ 10^logint(n, b));
(isok(n) = leadingdigit(fibonacci(n))==5);
(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, A105505.

Cf. A105511, A105512, A105513, A105514, A105516, A105517, A105518, A105519.

Sequence in context: A105516 A105518 A111896 * A105514 A214081 A194338

Adjacent sequences: A105512 A105513 A105514 * A105516 A105517 A105518

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2005

Status

approved