A354371 - OEIS

%I #15 Jun 25 2022 22:03:44

%S 1,2,3,4,12,5,6,7,14,11,16,8,10,13,17,19,22,9,15,20,26,27,69,31,18,40,

%T 34,32,42,78,49,21,24,30,41,43,46,51,33,23,25,39,37,44,64,68,59,54,48,

%U 28,29,38,58,74,70,72,92,52,63,36,35,87,101,98,80,82,84,177,121,65,60,45,96,53,103,76

%N Square array read by antidiagonals such that the sum of the digits inside any 2 X 2 square is itself a square.

%C This is the lexicographically earliest permutation of the positive integers with this property.

%e Array:

%e .

%e     1,   2,   4,   6,  16,  19,  27,  42,  46,  68,  72,  84, 120, 138, 156, ...

%e     3,  12,   7,   8,  22,  69,  78,  51,  59,  92, 177,  94, 134, 175, 165, ...

%e     5,  14,  10,   9,  31,  49,  33,  54,  52, 121, 132, 195, 166, 249, 162, ...

%e    11,  13,  15,  18,  21,  23,  48,  63,  65,  77,  75,  97, 131, 178, 171, ...

%e    17,  20,  40,  24,  25,  28,  36,  60,  55,  86,  81,  93, 169, 147, 174, ...

%e    26,  34,  30,  39,  29,  35,  45,  57,  62, 130,  90, 150, 200, 289, 303, ...

%e    32,  41,  37,  38,  87,  96,  89,  47,  50,  71, 186, 204, 146, 202, 205, ...

%e    43,  44,  58, 101,  53,  56, 105, 110,  61,  79,  73, 113, 149, 142, 198, ...

%e    64,  74,  98, 103,  83, 114,  67, 112,  66,  95, 108, 100, 140, 145, 194, ...

%e    70,  80,  76, 159, 123,  85, 179, 168,  99, 104, 107, 115, 129, 153, 210, ...

%e    82, 119, 188, 199, 117, 116, 128, 141,  91,  88, 106, 102, 158, 185, 163, ...

%e   109, 122, 111, 118, 137, 125, 126, 127, 136, 139, 148, 157, 213, 258, 172, ...

%e   124, 167, 176, 135, 222, 155, 143, 144, 133, 231, 197, 240, 164, 211, 214, ...

%e   151, 152, 184, 193, 161, 173, 298, 229, 160, 187, 154, 196, 201, 189, 223, ...

%e   170, 238, 267, 206, 232, 181, 180, 215, 224, 203, 212, 221, 183, 259, 233, ...

%e   ...

%e .

%e The sum of the digits inside the upper 2 X 2 squares is (1 + 2) + (3 + 1 + 2) = 9 (a square);

%e The sum of the digits inside the next horizontal 2 X 2 square is (2 + 4) + (1 + 2 + 7) = 16 (a square);

%e The sum of the digits inside the next horizontal 2 X 2 square is (4 + 6) + (7 + 8) = 25 (a square);

%e ...

%e The sum of the digits inside the 2nd vertical 2 X 2 square on the left is (3 + 1 + 2) + (5 + 1 + 4) = 16 (a square);

%e The sum of the digits inside the next vertical 2 X 2 square on the left is (5 + 1 + 4) + (1 + 1 + 1 + 3) = 16 (a square);

%e ...

%e The sum of the digits inside the lower right 2 X 2 square is (1 + 8 + 9) + (2 + 2 + 3) + (2 + 5 + 9) + (2 + 3 + 3) = 49 (a square); etc.

%Y Cf. A325785.

%K tabl,nonn

%O 1,2

%A _Eric Angelini_ and _Carole Dubois_, May 24 2022