A082648 Consider f(m) = Sum_{k=1..m} k! (A007489) when m is very large; a(n) = n-th digit from end.

3, 1, 3, 0, 4, 9, 0, 2, 4, 0, 2, 9, 8, 2, 5, 6, 3, 3, 2, 4, 4, 6, 5, 5, 2, 5, 0, 9, 3, 0, 5, 0, 1, 3, 9, 5, 3, 2, 3, 4, 0, 8, 4, 9, 9, 7, 0, 1, 1, 2, 6, 8, 3, 7, 4, 8, 6, 8, 7, 4, 9, 7, 4, 7, 4, 2, 2, 9, 0, 0, 4, 3, 3, 0, 5, 6, 5, 8, 6, 5

Offset: 1

Author

Alexander Adamchuk, May 15 2003

Keywords

• easy
• base
• nonn

Comments

Apart from the first term, the same as A025016. - R. J. Mathar, Sep 17 2008

Since A007845 gives the smallest factorial having at least n trailing zeros, the first n digits read from the right are determined for m >= A007845(n) - 1. - Martin Renner, Feb 14 2021

Examples

			Sum_{k=1..30} k! = 274410818470142134209703780940313.
The last 7 digits in reverse order give us the first 7 terms of this sequence: 3,1,3,0,4,9,0.
From _Jon E. Schoenfield_, Feb 16 2021: (Start)
The table below shows the 12 least-significant digits of Sum_{k=1..m} k! converging to the first 12 terms of this sequence (in reverse order) as m increases:
.
    m  Sum_{k=1..m} k!  # corresponding digits
   --  ---------------  ----------------------
    0                0                       0
    4               33                       1
    9           409113                       2
   14      93928268313                       3
   19  ...485935180313                       4
   24  ...567844940313                       6
   29  ...395300940313                       7
   34  ...323620940313                       8
   39  ...232420940313                       9
   44  ...080420940313                      10
   49  ...920420940313                      12
  ...
   oo  ...920420940313
(End)
		

Crossrefs

Cf. A007489, A003422, A007845, A045748.

Programs

Mathematica

Take[Reverse[IntegerDigits[Sum[n!, {n, 1, 500}]]], 100] (* generates first 100 terms *)