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A333993 Square spiral on a 2D square lattice, one term per cell, starting at the origin with 0; the integers forming a square of size k X k, for all k = 1, 2, 3, ..., add up to a number that does not contain the digit 1.

%I A333993 #15 Jun 27 2025 22:22:54
%S A333993 0,2,3,4,5,20,6,7,23,8,9,22,24,25,200,26,27,28,29,203,30,33,32,202,
%T A333993 2000,34,35,36,205,37,38,204,39,42,2002,40,43,90,59,84,46,2023,44,206,
%U A333993 53,82,48,220,284,45,57,74,207,47,85,2244,49,52,50,76,2043,273,20007,436,54,55,56,58,62,60,96
%N A333993 Square spiral on a 2D square lattice, one term per cell, starting at the origin with 0; the integers forming a square of size k X k, for all k = 1, 2, 3, ..., add up to a number that does not contain the digit 1.
%C A333993 This is the lexicographically earliest sequence of distinct nonnegative terms with this property. Computed in memory of Michaël Falcoz, Aug 20 2020.
%e A333993 No integer in the spiral contains "1"; the integers forming any 2 X 2 square add up to a number without "1"; the integers forming any 3 X 3 square add up to a number without "1", etc.
%e A333993 The 5 X 5 square visible here (without the leg 34-35) is made of 25 terms summing up to 2968, a result that doesn't use the digit 1.
%e A333993 .
%e A333993      30--33--32-202-2000-34
%e A333993       |                   |
%e A333993     203   6---7--23---8  35
%e A333993       |   |           |   .
%e A333993      29  20   0---2   9   .
%e A333993       |   |       |   |   .
%e A333993      28   5---4---3  22
%e A333993       |               |
%e A333993      27--26--200-25--24
%e A333993 .
%Y A333993 Cf. A337115.
%K A333993 base,nonn
%O A333993 1,2
%A A333993 _Eric Angelini_ and _Jean-Marc Falcoz_, Sep 04 2020