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

1,2

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.

Links

Table of n, a(n) for n=1..64.

Example

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

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 *)

Crossrefs

Cf. A000040, A107770, A333200.

Sequence in context: A176707 A257533 A308021 * A191707 A192177 A288417

Adjacent sequences: A333198 A333199 A333200 * A333202 A333203 A333204

Keyword

nonn,tabl

Author

Clark Kimberling, May 11 2020

Status

approved