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

Author

Carmine Suriano, Sep 26 2009

Keywords

• nonn

Comments

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

Examples

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

References

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

Links

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

Programs

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 *)

Formula

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

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

Extensions

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