A165753 Number of trailing zeros in sequence of factorials of Fibonacci numbers.

0, 0, 0, 0, 1, 1, 2, 4, 7, 13, 20, 34, 56, 93, 150, 244, 396, 643, 1043, 1689, 2733, 4425, 7161, 11587, 18754, 30344, 49100, 79449, 128552, 208007, 336563, 544573, 881140, 1425715, 2306860, 3732583, 6039449, 9772038, 15811490, 25583533, 41395029

Offset

1,7

Comments

a(n) is the number of zeros at rightmost place of F(n)!

References

C. Suriano, Miniature Matematiche, Il rosone, 2009, pp. 149-152.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = A027868(A000045(n))

a(n) = k * phi^n + O(n), for k = 1/sqrt(80).

Example

F(7)!=13!=6227020800 which ends with 2 zeros; therefore a(7)=2.

Mathematica

zOF[n_Integer?Positive]:=Module[{maxpow=0}, While[5^maxpow<=n, maxpow++]; Plus@@Table[Quotient[n, 5^i], {i, maxpow-1}]]; zOF[#]&/@ Fibonacci[ Range[ 50]] (* Harvey P. Dale, Jan 10 2020 *)

Crossrefs

Sequence in context: A347703 A112997 A037032 * A347779 A369520 A266650

Adjacent sequences: A165750 A165751 A165752 * A165754 A165755 A165756

Keyword

nonn

Author

Carmine Suriano, Sep 26 2009

Extensions

Extended and edited by Charles R Greathouse IV, Mar 23 2010

Status

approved