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