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A354441 Lexicographically earliest sequence of distinct positive integers on a square spiral such that any 3X3 square of numbers sums to a prime.

%I A354441 #13 May 30 2022 08:23:32
%S A354441 1,2,3,4,5,6,7,8,11,9,10,13,12,14,20,16,15,17,19,22,18,21,25,26,35,23,
%T A354441 24,27,28,30,29,31,33,37,41,36,32,34,43,38,40,52,39,42,66,48,45,44,46,
%U A354441 47,49,54,50,56,51,57,53,55,61,72,67,59,58,62,60,63,71,68,74,76,70,80,64,65,69,77,73
%N A354441 Lexicographically earliest sequence of distinct positive integers on a square spiral such that any 3X3 square of numbers sums to a prime.
%C A354441 See A354442 for the successive prime sums formed by each completed 3X3 square of numbers.
%H A354441 Scott R. Shannon, <a href="/A354441/a354441.png">Image of the first 4000 terms</a>. The green line is y = n.
%e A354441 The spiral begins
%e A354441                                 .
%e A354441                                 .
%e A354441    32--36--41--37--33--31--29  57
%e A354441     |                       |   |
%e A354441    34  15--16--20--14--12  30  51
%e A354441     |   |               |   |   |
%e A354441    43  17   5---4---3  13  28  56
%e A354441     |   |   |       |   |   |   |
%e A354441    38  19   6   1---2  10  27  50
%e A354441     |   |   |           |   |   |
%e A354441    40  22   7---8--11---9  24  54
%e A354441     |   |                   |   |
%e A354441    52  18--21--25--26--35--23  49
%e A354441     |                           |
%e A354441    39--42--66--48--45--44--46--47
%e A354441 .
%e A354441 .
%e A354441 a(9) = 11 as this completes a 3X3 square of numbers 5,4,3,6,1,2,7,8,11, which sum to 47, a prime, and 11 is the smallest unused number to form a prime sum.
%e A354441 a(12) = 13 as this completes a 3X3 square of numbers 8,11,9,1,2,10,4,3,13, which sum to 61, a prime, and 13 is the smallest unused number to form a prime sum.
%Y A354441 Cf. A354442, A337116, A257339, A354434, A000040.
%K A354441 nonn
%O A354441 1,2
%A A354441 _Scott R. Shannon_, May 29 2022