A061536 -id:A061536 - cp's OEIS frontend

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

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, 49, 68, 20, 21, 26, 31, 48, 55, 75, 83, 24, 25, 30, 36, 54, 61, 82, 91, 116, 28, 29, 35, 41, 60, 67, 90, 99, 125, 171, 33, 34, 40, 47, 66, 74, 98, 107, 134, 181

Offset: 1

Clark Kimberling, May 14 2016

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.

			Northwest corner:
1     2     4     6     9     12    16    20
3     5     7     10    13    17    21    25
8     11    14    18    22    26    30    35
15    19    23    27    31    36    41    47
32    37    42    48    54    60    66    73
43    49    55    61    67    74    81    89

Cf. A249727, A061536 (= row 1).

t = Flatten[Table[Range[PrimePi[n]], {n, 2, 200}]];
r[n_, k_] := Flatten[Position[t, n]][[k]]
TableForm[Table[r[n, k], {n, 1, 12}, {k, 1, 12}]]  (* A272616 array*)
Table[r[n - k + 1, k], {n, 15}, {k, n, 1, -1}] // Flatten  (* A272616 sequence*)

cp's OEIS Frontend

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

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