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A272616 Rectangular array, r(n,k), by antidiagonals: the interspersion associated with the fractal sequence A249727.

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