A354371 Square array read by antidiagonals such that the sum of the digits inside any 2 X 2 square is itself a square.

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..76.

Example

Array:
.
    1,   2,   4,   6,  16,  19,  27,  42,  46,  68,  72,  84, 120, 138, 156, ...
    3,  12,   7,   8,  22,  69,  78,  51,  59,  92, 177,  94, 134, 175, 165, ...
    5,  14,  10,   9,  31,  49,  33,  54,  52, 121, 132, 195, 166, 249, 162, ...
   11,  13,  15,  18,  21,  23,  48,  63,  65,  77,  75,  97, 131, 178, 171, ...
   17,  20,  40,  24,  25,  28,  36,  60,  55,  86,  81,  93, 169, 147, 174, ...
   26,  34,  30,  39,  29,  35,  45,  57,  62, 130,  90, 150, 200, 289, 303, ...
   32,  41,  37,  38,  87,  96,  89,  47,  50,  71, 186, 204, 146, 202, 205, ...
   43,  44,  58, 101,  53,  56, 105, 110,  61,  79,  73, 113, 149, 142, 198, ...
   64,  74,  98, 103,  83, 114,  67, 112,  66,  95, 108, 100, 140, 145, 194, ...
   70,  80,  76, 159, 123,  85, 179, 168,  99, 104, 107, 115, 129, 153, 210, ...
   82, 119, 188, 199, 117, 116, 128, 141,  91,  88, 106, 102, 158, 185, 163, ...
  109, 122, 111, 118, 137, 125, 126, 127, 136, 139, 148, 157, 213, 258, 172, ...
  124, 167, 176, 135, 222, 155, 143, 144, 133, 231, 197, 240, 164, 211, 214, ...
  151, 152, 184, 193, 161, 173, 298, 229, 160, 187, 154, 196, 201, 189, 223, ...
  170, 238, 267, 206, 232, 181, 180, 215, 224, 203, 212, 221, 183, 259, 233, ...
  ...
.
The sum of the digits inside the upper 2 X 2 squares is (1 + 2) + (3 + 1 + 2) = 9 (a square);
The sum of the digits inside the next horizontal 2 X 2 square is (2 + 4) + (1 + 2 + 7) = 16 (a square);
The sum of the digits inside the next horizontal 2 X 2 square is (4 + 6) + (7 + 8) = 25 (a square);
...
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);
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);
...
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.

Crossrefs

Cf. A325785.

Sequence in context: A176621 A370365 A099527 * A345276 A096864 A373576

Adjacent sequences: A354368 A354369 A354370 * A354372 A354373 A354374

Keyword

tabl,nonn

Author

Eric Angelini and Carole Dubois, May 24 2022

Status

approved