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A337117 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 palindrome.

%I A337117 #20 Aug 20 2020 20:45:59
%S A337117 0,1,2,3,4,15,5,13,8,6,7,12,9,10,18,19,11,21,26,20,14,16,32,24,17,22,
%T A337117 43,45,35,55,23,34,46,25,37,44,27,29,38,36,39,28,30,49,42,31,54,56,66,
%U A337117 33,40,76,48,53,59,65,41,52,62,60,50,69,72,79,47,89,57,67,61,86,99
%N A337117 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 palindrome.
%C A337117 This is the lexicographically earliest permutation of the nonnegative integers with this property.
%H A337117 Jean-Marc Falcoz, <a href="/A337117/b337117.txt">Table of n, a(n) for n = 1..2757</a>
%e A337117 The four integers inside each of the four 2 X 2 squares that contain 0 sum up to a palindrome: 0+1+2+3=6 / 0+3+4+15=22 / 0+15+5+13=33 / 0+13+8+1=22. This is true for any 2 X 2 square picked up on the (infinite) grid: the upper right corner below sums up to 88 for instance (17+22+43+6).
%e A337117 .
%e A337117      14--16--32--24--17--22
%e A337117       |                   |
%e A337117      20   5--13-- 8---6  43
%e A337117       |   |           |
%e A337117      26  15   0---1   7
%e A337117       |   |       |   |
%e A337117      21   4---3---2  12
%e A337117       |               |
%e A337117      11--19--18--10-- 9
%e A337117 .
%Y A337117 Cf. A214176, A337116 (same idea, with primes instead of palindromes), A337115 (squares instead of palindromes).
%K A337117 base,nonn
%O A337117 1,3
%A A337117 _Eric Angelini_ and _Jean-Marc Falcoz_, Aug 16 2020