A105517 Number of times 7 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, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 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, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset

0,45

Links

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

Formula

a(n) = #{k: A008963(k) = 7 and 0<=k<=n};

a(A105507(n)) = a(A105507(n) - 1) + 1;

n = A105511(n) + A105512(n) + A105513(n) + A105514(n) + A105515(n) + A105516(n) + a(n) + A105518(n) + A105519(n).

a(n) ~ log_10(8/7) * n. - Amiram Eldar, Jan 12 2023

Mathematica

Accumulate[Table[If[IntegerDigits[Fibonacci[n]][[1]]==7, 1, 0], {n, 0, 120}]] (* Harvey P. Dale, Apr 29 2018 *)

Prog

(PARI)
(leadingdigit(n, b=10) = n \ 10^logint(n, b));
(isok(n) = leadingdigit(fibonacci(n))==7);
(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, A105507.

Cf. A105511, A105512, A105513, A105514, A105515, A105516, A105518, A105519.

Sequence in context: A319816 A343437 A348242 * A230774 A056813 A125269

Adjacent sequences: A105514 A105515 A105516 * A105518 A105519 A105520

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2005

Status

approved