A105512 Number of times 2 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.

0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16

Offset

0,9

Links

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

Formula

a(n) = #{k: A008963(k) = 2 and 0<=k<=n};

a(A105502(n)) = a(A105502(n) - 1) + 1;

n = A105511(n) + a(n) + A105513(n) + A105514(n) + A105515(n) + A105516(n) + A105517(n) + A105518(n) + A105519(n).

a(n) ~ log_10(3/2) * n. - Amiram Eldar, Jan 12 2023

Mathematica

Accumulate[Table[If[IntegerDigits[Fibonacci[n]][[1]] == 2, 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))==2);
(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, A105502.

Cf. A105511, A105513, A105514, A105515, A105516, A105517, A105518, A105519.

Sequence in context: A104355 A235402 A092278 * A301506 A002266 A075249

Adjacent sequences: A105509 A105510 A105511 * A105513 A105514 A105515

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2005

Status

approved