A045748 a(n) is the number consisting of the last n digits (although any leading 0's among those last n digits are omitted) of Sum_{j=1..k} j! for all sufficiently large k.

3, 13, 313, 313, 40313, 940313, 940313, 20940313, 420940313, 420940313, 20420940313, 920420940313, 8920420940313, 28920420940313, 528920420940313, 6528920420940313, 36528920420940313, 336528920420940313, 2336528920420940313, 42336528920420940313

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• base

Examples

			Look at A007489, the partial sums of the factorials. The last digit stabilizes at 3, so a(1) = 3.  The last two digits stabilize at 13, so a(2) = 13. - _N. J. A. Sloane_, Mar 22 2021
		

Crossrefs

Cf. A007489, A082648.

Formula

a(n) = (Sum_{k>=1} k!) mod 10^n. - Sean A. Irvine, Mar 19 2021