A105515 - OEIS

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

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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 *)