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%I #28 May 17 2016 09:18:53
%S 1,2,3,4,5,8,6,7,11,15,9,10,14,19,32,12,13,18,23,37,43,16,17,22,27,42,
%T 49,68,20,21,26,31,48,55,75,83,24,25,30,36,54,61,82,91,116,28,29,35,
%U 41,60,67,90,99,125,171,33,34,40,47,66,74,98,107,134,181
%N Rectangular array, r(n,k), by antidiagonals: the interspersion associated with the fractal sequence A249727.
%C r(n,k) is the position of the k-th occurrence of n in A249727. Every positive integer occurs exactly once, and each row is interspersed by each other row, except for initial terms.
%e Northwest corner:
%e 1 2 4 6 9 12 16 20
%e 3 5 7 10 13 17 21 25
%e 8 11 14 18 22 26 30 35
%e 15 19 23 27 31 36 41 47
%e 32 37 42 48 54 60 66 73
%e 43 49 55 61 67 74 81 89
%t t = Flatten[Table[Range[PrimePi[n]], {n, 2, 200}]];
%t r[n_, k_] := Flatten[Position[t, n]][[k]]
%t TableForm[Table[r[n, k], {n, 1, 12}, {k, 1, 12}]] (* A272616 array*)
%t Table[r[n - k + 1, k], {n, 15}, {k, n, 1, -1}] // Flatten (* A272616 sequence*)
%Y Cf. A249727, A061536 (= row 1).
%K nonn,tabl,easy
%O 1,2
%A _Clark Kimberling_, May 14 2016