A337115 Square spiral on a 2D square lattice, one term per cell, starting at the origin with 0; the four integers forming any 2 X 2 square add up to a square.

0, 1, 2, 6, 3, 7, 4, 5, 10, 8, 17, 16, 9, 22, 19, 21, 11, 14, 12, 13, 15, 32, 23, 26, 20, 18, 35, 40, 27, 29, 24, 38, 31, 28, 53, 36, 25, 49, 47, 48, 71, 45, 30, 54, 43, 46, 74, 76, 55, 33, 63, 80, 41, 61, 52, 39, 34, 72, 62, 65, 101, 107, 60, 75, 37, 59, 92, 68, 93, 44, 96

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Aug 16 2020

Keywords

• nonn

Comments

This is (by definition) the lexicographically earliest permutation of the nonnegative integers with this property.

Examples

			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 + 10 + 1 = 16. This is true for any 2 X 2 square on the (infinite) grid: the upper right corner below adds up to  81 (= 20 + 18 + 35 + 8), for instance.
.
     15--32--23--26--20--18
      |                   |
     13   4---5--10---8  35
      |   |           |   .
     12   7   0---1  17   .
      |   |       |   |   .
     14   3---6---2  16
      |               |
     11--21--19--22---9
.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..2757

Crossrefs

Cf. A214176, A337116 (same idea, with primes rather than squares), A337117 (with palindromes), A337368 (with pandigitals).