A333201 Rectangular array read by antidiagonals: row n shows the numbers k such that p(k) = prime(k-1) + 2n, where prime(k) = k-th prime, with 1 prefixed to row 1.

1, 2, 5, 3, 7, 10, 4, 9, 12, 25, 6, 13, 16, 73, 35, 8, 15, 17, 78, 43, 47, 11, 20, 19, 80, 54, 48, 31, 14, 23, 22, 88, 62, 92, 63, 283, 18, 26, 24, 93, 69, 98, 67, 296, 100, 21, 28, 33, 95, 81, 115, 138, 320, 181, 155, 27, 30, 37, 125, 83, 122, 147, 332, 206

Offset: 1

Author

Clark Kimberling, May 11 2020

Keywords

• nonn
• tabl

Comments

Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers. Row 1: A107770, except for initial 1,2.

Examples

			Northwest corner:
    1      2     3     4     6    8    11   14   18   21
    5      7     9    13    15   20    23   26   28   30
   10     12    16    17    19   22    24   33   37   38
   25     73    78    80    88   93    95  125  127  129
   35     43    54    62    69   81    83  102  107  116
		

Crossrefs

Cf. A000040, A107770, A333200.

Programs

Mathematica

z = 2700; p = Prime[Range[z]];
r[n_] := Select[Range[z], p[[#]] - p[[# - 1]] == 2 n &]; r[1] = Join[{1, 2}, r[1]];
TableForm[Table[Prime[r[n]], {n, 1, 18}]]  (* A333200, array *)
TableForm[Table[r[n], {n, 1, 18}]] (* A333201, array *)
Table[Prime[r[n - k + 1][[k]]], {n, 12}, {k, n, 1, -1}] // Flatten (* A333200, sequence *)
Table[r[n - k + 1][[k]], {n, 12}, {k, n, 1, -1}] // Flatten (* A333201, sequence *)