A173558 a(n) is the smallest number whose factorial has 10^n trailing zeros.

5, 45, 405, 4005, 40010, 400005, 4000005, 40000010, 400000015, 4000000015, 40000000015, 400000000015, 4000000000010, 40000000000015, 400000000000020, 4000000000000025, 40000000000000025, 400000000000000025

Offset: 0

Author

José María Grau Ribas, Feb 21 2010

Keywords

• base
• nonn

Examples

			4!=24 has no zeros, and 5!=120 has 1 (10^0) zero ==> a(0)= 5.
44!=2658271574788448768043625811014615890319638528000000000 (9 zeros) and 45!=119622220865480194561963161495657715064383733760000000000 (10^1= 10 zeros) ==> a(1)=45.
		

Links

• A. M. Oller-Marcen, J. Maria Grau, On the Base-b Expansion of the Number of Trailing Zeros of b^k!, J. Int. Seq. 14 (2011) 11.6.8

Crossrefs

If A173292(n)> -1 then a(n)=A173292(n)

Programs

Mathematica

Z10[n_] := Floor[Sum[Floor[n/5^i], {i, 1, Floor[Log[5, n]]}]]; a[n_] := Module[{m = 4*10^n}, While[Z10[m] < 10^n, m++ ]; m]; Table[a[n], {n, 0, 60}]