%I #10 Aug 20 2023 12:13:47
%S 1,2,3,4,5,7,8,6,11,15,16,10,9,23,31,32,12,14,13,47,63,64,20,18,17,19,
%T 95,127,128,24,22,25,21,27,191,255,256,40,28,26,33,29,39,383,511,512,
%U 48,36,30,38,37,35,55,767,1023,1024,80,44,34,42,41,51,43,79,1535,2047
%N Square array A(n, k), n, k > 0, read and filled in the greedy way by downwards antidiagonals with distinct positive integers such that for any v > 0, the value 2*v appears in the same row as the value v, and the value 2*v + 1 appears in the same column as the value v.
%C As a flat sequence, this is a permutation of the positive integers with inverse A364775.
%H Rémy Sigrist, <a href="/A364772/a364772.png">Colored representation of the parity of A(n, k) for n, k <= 1000</a> (where black pixels denote odd terms)
%H Rémy Sigrist, <a href="/A364772/a364772.gp.txt">PARI program</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A(1, k) = 2^(k-1).
%F A(n, 1) = 2^n - 1.
%e Array A(n, k) begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12
%e ---+--------------------------------------------------------------
%e 1| 1 2 4 8 16 32 64 128 256 512 1024 2048
%e 2| 3 5 6 10 12 20 24 40 48 80 96 160
%e 3| 7 11 9 14 18 22 28 36 44 56 72 88
%e 4| 15 23 13 17 25 26 30 34 46 50 52 60
%e 5| 31 47 19 21 33 38 42 62 66 76 84 94
%e 6| 63 95 27 29 37 41 49 54 58 74 82 98
%e 7| 127 191 39 35 51 45 57 69 70 78 90 102
%e 8| 255 383 55 43 67 53 61 73 86 101 105 106
%e 9| 511 767 79 59 75 65 85 81 89 113 118 121
%e 10| 1023 1535 111 71 103 77 99 109 93 142 145 154
%e 11| 2047 3071 159 87 135 83 115 125 97 149 165 166
%e 12| 4095 6143 223 119 151 91 123 139 117 153 169 177
%o (PARI) See Links section.
%Y Cf. A364775 (inverse).
%K nonn,tabl
%O 1,2
%A _Rémy Sigrist_, Aug 06 2023