A354373 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 prime.

0, 1, 2, 4, 3, 6, 5, 8, 11, 7, 9, 10, 12, 14, 15, 13, 16, 18, 23, 21, 17, 25, 27, 19, 22, 20, 24, 34, 33, 30, 26, 32, 28, 35, 29, 36, 31, 38, 37, 41, 40, 44, 39, 45, 43, 42, 48, 47, 51, 46, 49, 53, 55, 59, 60, 57, 50, 66, 75, 64, 54, 58, 62, 71, 52, 73, 79, 82, 84, 80, 56, 88, 61, 93, 68, 65, 67, 91

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:
.
     17--25--27--19--22--20
      |                   |
     21   5---8--11---7  24
      |   |           |   .
     23   6   0---1   9   .
      |   |       |   |   .
     18   3---4---2  10
      |               |
     16--13--15--14--12
.
The digits of the four integers inside each of the four 2 X 2 squares that contain the initial 0 add up to a prime: 0 + 1 + 2 + 4 = 7, 0 + 4 + 3 + 6 = 13, 0 + 6 + 5 + 8 = 19, 0 + 8 + (1+1) + 1 = 11. This is true for any 2 X 2 square on the (infinite) grid; the upper right corner adds up to 19, for instance: (2+2) + (2+0) + (2+4) + 7 = 19; etc.
		

Crossrefs

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