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

Author

Clark Kimberling, May 14 2016

Keywords

• nonn
• tabl
• easy

Comments

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.

Examples

			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
		

Crossrefs

Cf. A249727, A061536 (= row 1).

Programs

Mathematica

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*)