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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.

%I A333201 #16 Jul 20 2020 02:06:46
%S A333201 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,
%T A333201 48,31,14,23,22,88,62,92,63,283,18,26,24,93,69,98,67,296,100,21,28,33,
%U A333201 95,81,115,138,320,181,155,27,30,37,125,83,122,147,332,206
%N 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.
%C A333201 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.
%e A333201 Northwest corner:
%e A333201     1      2     3     4     6    8    11   14   18   21
%e A333201     5      7     9    13    15   20    23   26   28   30
%e A333201    10     12    16    17    19   22    24   33   37   38
%e A333201    25     73    78    80    88   93    95  125  127  129
%e A333201    35     43    54    62    69   81    83  102  107  116
%t A333201 z = 2700; p = Prime[Range[z]];
%t A333201 r[n_] := Select[Range[z], p[[#]] - p[[# - 1]] == 2 n &]; r[1] = Join[{1, 2}, r[1]];
%t A333201 TableForm[Table[Prime[r[n]], {n, 1, 18}]]  (* A333200, array *)
%t A333201 TableForm[Table[r[n], {n, 1, 18}]] (* A333201, array *)
%t A333201 Table[Prime[r[n - k + 1][[k]]], {n, 12}, {k, n, 1, -1}] // Flatten (* A333200, sequence *)
%t A333201 Table[r[n - k + 1][[k]], {n, 12}, {k, n, 1, -1}] // Flatten (* A333201, sequence *)
%Y A333201 Cf. A000040, A107770, A333200.
%K A333201 nonn,tabl
%O A333201 1,2
%A A333201 _Clark Kimberling_, May 11 2020