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A338644 Square spiral of smallest distinct positive integers starting at 1 such that the four sums of each term with its four nearest neighbors is a prime number.

%I A338644 #11 Apr 26 2021 21:33:23
%S A338644 1,2,3,4,7,6,5,12,11,8,9,10,13,16,15,22,19,24,17,14,23,18,25,36,35,26,
%T A338644 21,20,27,34,33,28,31,52,37,42,29,54,43,30,53,44,39,50,89,48,61,66,41,
%U A338644 32,47,62,51,46,55,76,63,38,45,58,49,60,67,72,59,68,83,84,73,78,95,98,65,74,57,92
%N A338644 Square spiral of smallest distinct positive integers starting at 1 such that the four sums of each term with its four nearest neighbors is a prime number.
%e A338644 The square spiral starts:
%e A338644 .
%e A338644      29--42--37--52--31--28--33
%e A338644       |                       |
%e A338644      54  19--22--15--16--13  34
%e A338644       |   |               |   |
%e A338644      43  24   7---4---3  10  27
%e A338644       |   |   |       |   |   |
%e A338644      30  17   6   1---2   9  20
%e A338644       |   |   |           |   |
%e A338644      53  14   5--12--11---8  21
%e A338644       |   |                   |
%e A338644      44  23--18--25--36--35--26
%e A338644       |
%e A338644      39--50--89--48--61--66--41..
%e A338644 .
%e A338644 a(2) = 2 as a(1) + 2 = 1 + 2 = 3, the smallest possible prime number.
%e A338644 a(3) = 3 as a(2) + 3 = 2 + 3 = 5, the next smallest possible prime number.
%e A338644 a(5) = 7 as a(4) + 7 = 4 + 7 = 11. Note a(5) cannot be 5 or 6 as when these are added to 4 the result is a composite number.
%e A338644 a(9) = 11 as a(8) + 11 = 12 + 11 = 23, and a(2) + 11 = 2 + 11 = 13, both being prime.
%Y A338644 Cf. A338642 (sum to composites), A000040, A063826, A260643, A334742, A307834, A338221.
%K A338644 nonn
%O A338644 1,2
%A A338644 _Scott R. Shannon_ and _Eric Angelini_, Apr 21 2021