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A344659 Lexicographically earliest sequence of distinct nonnegative terms on a square spiral such that each term forms no prime value in the eight sums when each term is added to each of its eight nearest neighbors.

%I A344659 #25 May 27 2021 06:23:33
%S A344659 0,1,8,14,4,6,9,15,20,5,7,13,2,12,10,11,16,22,18,3,17,19,25,29,28,21,
%T A344659 23,27,31,26,24,30,32,34,35,33,36,41,40,42,39,37,38,43,45,47,49,53,57,
%U A344659 48,51,54,61,50,44,46,52,56,58,60,59,65,55,62,63,70,64,74,66,69,67,68,72,73,77,71,75
%N A344659 Lexicographically earliest sequence of distinct nonnegative terms on a square spiral such that each term forms no prime value in the eight sums when each term is added to each of its eight nearest neighbors.
%C A344659 .
%C A344659   36--33--35--34--32--30--24
%C A344659    |                       |
%C A344659   41  16--11--10--12---2  26
%C A344659    |   |               |   |
%C A344659   40  22   4--14---8  13  31
%C A344659    |   |   |       |   |   |
%C A344659   42  18   6   0---1   7  27
%C A344659    |   |   |           |   |
%C A344659   39   3   9--15--20---5  23   .
%C A344659    |   |                   |   .
%C A344659   37  17--19--25--29--28--21   .
%C A344659    |                           |
%C A344659   38--43--45--47--49--53--57--48
%C A344659 .
%e A344659 The eight terms that are in contact with the initial zero are 1, 8, 14, 4, 6, 9, 15, 20: none of them is prime [forcing the sum a(k) + 0 to be nonprime, with k<9]; more generally, no term of the square spiral when added to any of its eight nearest neighbors sums to a prime.
%Y A344659 Cf. A063826, A344660, A002808, A000040.
%K A344659 nonn
%O A344659 1,3
%A A344659 _Eric Angelini_ and _Scott R. Shannon_, May 26 2021