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 antidiagonals downward.

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

1,1

Comments

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

Links

Table of n, a(n) for n=1..65.

Formula

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

T(1,k) = k+1.

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

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

Example

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.

Sequence in context: A328739 A304088 A286597 * A358552 A317713 A341041

Adjacent sequences: A358664 A358665 A358666 * A358668 A358669 A358670

Keyword

nonn,tabl

Author

Jon E. Schoenfield, Nov 25 2022

Status

approved