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Array A read by antidiagonals: A(n,k) = n-th digit of the base k expansion of 1/n.
4

%I #10 Jul 31 2019 20:59:19

%S 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,2,1,2,0,0,0,0,0,0,1,0,0,0,3,0,1,0,1,

%T 0,0,0,0,0,2,0,0,2,0,0,0,4,2,5,1,4,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,5,

%U 3,2,1,1,0,3,3,0,0,0,0,1,0,1,3,0,0,2,1,0,3,0,0,0,6,0,8,0,4,1,6,0

%N Array A read by antidiagonals: A(n,k) = n-th digit of the base k expansion of 1/n.

%e A(10,9) = 8, as the 10th digit of the base 9 expansion of 1/10 = 0.0808080808080808080808080808... is 8.

%e Array A(n, k) begins:

%e n\k 1 2 3 4 5 6 7 8 9 10

%e 1 0 0 0 0 0 0 0 0 0 0

%e 2 0 0 1 0 2 0 3 0 4 0

%e 3 0 0 0 1 1 0 2 2 0 3

%e 4 0 0 2 0 1 0 5 0 2 0

%e 5 0 0 0 0 0 1 1 1 1 0

%e 6 0 0 1 2 4 0 1 2 4 6

%e 7 0 0 0 0 0 0 0 1 1 1

%e 8 0 0 1 0 3 0 6 0 1 0

%e 9 0 0 0 3 3 0 3 0 0 1

%e 10 0 0 0 1 2 3 4 6 8 0

%t a = {}; l = 100; x = Table[ Join[Range[2n - 1], Reverse@ Range[2n - 2]], {n, l}] // Flatten; y = Table[ Join[Range[2m], Reverse@Range[2m - 1]], {m, l-1}] // Flatten; Do[a = Append[a, Mod[ Floor[1/Part[x, i] * Part[y,i]^Part[x, i]], Part[y,i]] ], {i, 1, l} ]; a

%Y Supersequence of A061480.

%Y Cf. A092542, A092543.

%K nonn,tabl,base,easy

%O 1,17

%A _Derek J. Graves_, Dec 06 2018, on behalf of _Joseph A. Stocke_