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%I #28 Aug 30 2020 02:29:43
%S 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,
%T 35,40,27,29,24,38,31,28,53,36,25,49,47,48,71,45,30,54,43,46,74,76,55,
%U 33,63,80,41,61,52,39,34,72,62,65,101,107,60,75,37,59,92,68,93,44,96
%N 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.
%C This is (by definition) the lexicographically earliest permutation of the nonnegative integers with this property.
%H Jean-Marc Falcoz, <a href="/A337115/b337115.txt">Table of n, a(n) for n = 1..2757</a>
%e 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.
%e .
%e 15--32--23--26--20--18
%e | |
%e 13 4---5--10---8 35
%e | | | .
%e 12 7 0---1 17 .
%e | | | | .
%e 14 3---6---2 16
%e | |
%e 11--21--19--22---9
%e .
%Y Cf. A214176, A337116 (same idea, with primes rather than squares), A337117 (with palindromes), A337368 (with pandigitals).
%K nonn
%O 1,3
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Aug 16 2020
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