A354372 Square spiral on a 2D square lattice, one term per cell, starting at the origin with 0; the digits of the four integers forming any 2 X 2 square add up to a square.

0, 1, 2, 6, 3, 7, 4, 5, 12, 8, 13, 9, 10, 22, 31, 21, 11, 17, 16, 25, 14, 18, 34, 19, 40, 15, 43, 24, 33, 27, 20, 49, 52, 28, 26, 30, 23, 42, 36, 39, 37, 59, 29, 51, 32, 69, 89, 41, 46, 35, 48, 38, 57, 66, 45, 50, 44, 55, 47, 99, 68, 98, 53, 54, 56, 65, 77, 61, 62, 60, 105, 104, 58, 70, 75, 67, 79

Offset: 1

Author

Eric Angelini and Carole Dubois, May 24 2022

Keywords

• base
• nonn

Comments

This is the earliest permutation of the nonnegative integers with this property.

Examples

			The spiral begins:
.
     14--18--34--19--40--15
      |                   |
     25   4---5--12---8  43
      |   |           |   .
     16   7   0---1  13   .
      |   |       |   |   .
     17   3---6---2   9
      |               |
     11--21--31--22--10
.
The digits of the four integers inside each of the four 2 X 2 squares that contain the initial 0 add up to a square: 0 + 1 + 2 + 6 = 9, 0 + 6 + 3 + 7 = 16, 0 + 7 + 4 + 5 = 16, 0 + 5 + (1+2) + 1 = 9. This is true for any 2 X 2 square on the (infinite) grid; the upper right corner adds up to 25, for instance: (4+0) + (1+5) + 8 + (4+3) = 25; etc.
		

Crossrefs

Cf. A337115, A337116, A337117, A337368, A354372.