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

1,2

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.

Links

Table of n, a(n) for n=1..65.

Example

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

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*)

Crossrefs

Cf. A249727, A061536 (= row 1).

Sequence in context: A194067 A191710 A194061 * A356419 A364775 A085176

Adjacent sequences: A272613 A272614 A272615 * A272617 A272618 A272619

Keyword

nonn,tabl,easy

Author

Clark Kimberling, May 14 2016

Status

approved