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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)