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A333200 Rectangular array read by antidiagonals: row n shows the primes p(k) such that p(k) = p(k-1) + 2n, with 2 prefixed to row 1.

%I A333200 #5 Jun 14 2020 22:49:41
%S A333200 2,3,11,5,17,29,7,23,37,97,13,41,53,367,149,19,47,59,397,191,211,31,
%T A333200 71,67,409,251,223,127,43,83,79,457,293,479,307,1847,61,101,89,487,
%U A333200 347,521,331,1949,541,73,107,137,499,419,631,787,2129,1087,907,103,113
%N A333200 Rectangular array read by antidiagonals: row n shows the primes p(k) such that p(k) = p(k-1) + 2n, with 2 prefixed to row 1.
%C A333200 Every prime occurs exactly once.
%C A333200 Row 1: A001632, except for initial term
%C A333200 Row 2: A046132
%C A333200 Row 3: A031925
%C A333200 Row 4: A031927
%C A333200 Row 5: A031929
%C A333200 Column 1: A006512, beginning with 5,7,13
%e A333200 Northwest corner:
%e A333200     2   3     5    7   13   19   31   43   61   73  103
%e A333200    11   17   23   41   47   71   83  101  107  113  131
%e A333200    29   37   53   59   67   79   89  137  157  163  173
%e A333200    97  367  397  409  457  487  499  691  709  727  751
%e A333200   149  191  251  293  347  419  431  557  587  641  701
%t A333200 z = 2700; p = Prime[Range[z]];
%t A333200 r[n_] := Select[Range[z], p[[#]] - p[[# - 1]] == 2 n &]; r[1] = Join[{1, 2}, r[1]];
%t A333200 TableForm[Table[Prime[r[n]], {n, 1, 18}]]  (* A333200, array *)
%t A333200 TableForm[Table[r[n], {n, 1, 18}]] (* A333201, array *)
%t A333200 Table[Prime[r[n - k + 1][[k]]], {n, 12}, {k, n, 1, -1}] // Flatten (* A333200, sequence *)
%t A333200 Table[r[n - k + 1][[k]], {n, 12}, {k, n, 1, -1}] // Flatten (* A333201, sequence *)
%Y A333200 Cf. A333201, A000040, A001632, A006512.
%K A333200 nonn,tabl
%O A333200 1,1
%A A333200 _Clark Kimberling_, May 09 2020