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%I #6 Nov 25 2022 22:13:08
%S 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,
%T 9,194,10,1521,1007,9,11,3,10,200,11,6034,4938,10,4433,12,2,11,375,13,
%U 6052,24709,13,30810,125,18,2,12,1517,16,96867,24733,51,216613,1014,1503,3
%N 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.
%C T(11,1) is unknown at this time.
%F T(n,1) = A358633(n).
%F T(1,k) = k+1.
%F T(2,k) = A095412(k+2).
%F T(3,k) = A118872(k+2).
%e Table begins:
%e .
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 ...
%e ---+------------------------------------------------------------------
%e 1 | 2 3 4 5 6 7 8 9 10 11 12 ...
%e 2 | 2 3 9 36 85 176 194 200 375 1517 ...
%e 3 | 2 3 4 5 9 10 11 13 16 ...
%e 4 | 18 88 97 100 1521 6034 6052 96867 ...
%e 5 | 8 208 977 1007 4938 24709 24733 ...
%e 6 | 7 8 9 10 13 51 ...
%e 7 | 4 11 4433 30810 216613 ...
%e 8 | 3 12 125 1014 ...
%e 9 | 2 18 1503 ...
%e 10 | 2 3 ...
%e 11 | ? ...
%e ... | ...
%Y Cf. A095412, A118872, A358633.
%K nonn,tabl
%O 1,1
%A _Jon E. Schoenfield_, Nov 25 2022