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

1,1

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

Links

Table of n, a(n) for n=1..80.

Example

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)

Mathematica

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

Crossrefs

Cf. A007489, A003422, A007845, A045748.

Sequence in context: A349004 A127549 A191009 * A174233 A079530 A020815

Adjacent sequences: A082645 A082646 A082647 * A082649 A082650 A082651

Keyword

easy,base,nonn

Author

Alexander Adamchuk, May 15 2003

Status

approved