A358667 T(n,k) is the k-th integer j > 1 such that the sum of digits of n^j is a power of n (or -1 if no such k-th integer exists); table read by downward antidiagonals.

2, 3, 2, 4, 3, 2, 5, 9, 3, 18, 6, 36, 4, 88, 8, 7, 85, 5, 97, 208, 7, 8, 176, 9, 100, 977, 8, 4, 9, 194, 10, 1521, 1007, 9, 11, 3, 10, 200, 11, 6034, 4938, 10, 4433, 12, 2, 11, 375, 13, 6052, 24709, 13, 30810, 125, 18, 2, 12, 1517, 16, 96867, 24733, 51, 216613, 1014, 1503, 3

Offset: 1

Author

Jon E. Schoenfield, Nov 25 2022

Keywords

• nonn
• tabl

Comments

T(11,1) is unknown at this time.

Examples

			Table begins:
.
   n\k|   1    2     3     4      5     6     7     8    9    10   11 ...
   ---+------------------------------------------------------------------
    1 |   2    3     4     5      6     7     8     9   10    11   12 ...
    2 |   2    3     9    36     85   176   194   200  375  1517  ...
    3 |   2    3     4     5      9    10    11    13   16   ...
    4 |  18   88    97   100   1521  6034  6052 96867  ...
    5 |   8  208   977  1007   4938 24709 24733   ...
    6 |   7    8     9    10     13    51   ...
    7 |   4   11  4433 30810 216613   ...
    8 |   3   12   125  1014    ...
    9 |   2   18  1503   ...
   10 |   2    3   ...
   11 |   ?  ...
  ... | ...
		

Crossrefs

Cf. A095412, A118872, A358633.

Formula

T(n,1) = A358633(n).

T(1,k) = k+1.

T(2,k) = A095412(k+2).

T(3,k) = A118872(k+2).