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%I #9 Jun 25 2022 22:03:58
%S 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,
%T 43,24,33,27,20,49,52,28,26,30,23,42,36,39,37,59,29,51,32,69,89,41,46,
%U 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
%N 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.
%C This is the earliest permutation of the nonnegative integers with this property.
%e The spiral begins:
%e .
%e 14--18--34--19--40--15
%e | |
%e 25 4---5--12---8 43
%e | | | .
%e 16 7 0---1 13 .
%e | | | | .
%e 17 3---6---2 9
%e | |
%e 11--21--31--22--10
%e .
%e 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.
%Y Cf. A337115, A337116, A337117, A337368, A354372.
%K base,nonn
%O 1,3
%A _Eric Angelini_ and _Carole Dubois_, May 24 2022
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