A349403 Sum of the digits of Sum_{k=1..n} k!.

0, 1, 3, 9, 6, 9, 18, 18, 18, 18, 27, 36, 36, 54, 54, 36, 45, 45, 72, 72, 63, 81, 99, 99, 117, 108, 99, 126, 126, 144, 117, 162, 144, 153, 171, 171, 153, 180, 180, 198, 171, 225, 207, 252, 225, 261, 261, 252, 270, 234, 270, 261, 279, 324, 324, 306, 342, 333, 333, 297, 351, 360, 351, 333, 387, 405, 369

Offset

0,3

Comments

If n > 4, then 9 divides a(n).

Links

Table of n, a(n) for n=0..66.

Formula

a(n) = A007953(A007489(n)).

a(n) = A127554(n+1) - 1 for n > 3.

Example

   n |  A007489 | A003422 | a(n) | A127554 |
-----+----------+---------+------+---------+
   0 |        0 |       0 |    0 |       0 |
   1 |        1 |       1 |    1 |       1 |
   2 |        3 |       2 |    3 |       2 |
   3 |        9 |       4 |    9 |       4 |
   4 |       33 |      10 |    6 |       1 |
   5 |      153 |      34 |    9 |       7 |
   6 |      873 |     154 |   18 |      10 |
   7 |     5913 |     874 |   18 |      19 |
   8 |    46233 |    5914 |   18 |      19 |
   9 |   409113 |   46234 |   18 |      19 |
  10 |  4037913 |  409114 |   27 |      19 |
  11 | 43954713 | 4037914 |   36 |      28 |

Mathematica

Table[Total[IntegerDigits[Sum[k!, {k, n}]]], {n, 0, 66}] (* Stefano Spezia, Nov 16 2021 *)

Prog

(PARI) a(n) = sumdigits(sum(k=1, n, k!));

Crossrefs

Cf. A004152, A007489, A007953, A127554.

Sequence in context: A343864 A309613 A189272 * A131954 A154593 A283439

Adjacent sequences: A349400 A349401 A349402 * A349404 A349405 A349406

Keyword

nonn,base

Author

Seiichi Manyama, Nov 15 2021

Status

approved