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%I #13 Mar 22 2023 08:06:27
%S 1,2,4,7,12,14,16,22,27,10,31,40,39,46,47,20,45,52,61,60,18,80,68,81,
%T 82,70,89,94,83,48,62,105,100,69,117,25,111,129,127,124,143,106,112,
%U 132,155,119,126,128,63,56,157,158,107,178,193,168,118,170,55,195,189,197,192,206,182,211,202
%N Lexicographically earliest sequence of distinct positive numbers on a square spiral such that the eight sums of each number with its eight nearest neighbors are distinct across the entire spiral and no number on the spiral equals any such sum.
%H Scott R. Shannon, <a href="/A361724/a361724_1.png">Image of the first 50000 terms</a>. The green line is a(n) = n.
%H Scott R. Shannon, <a href="/A361724/a361724.png">Image of the first 50000 terms on the square spiral</a>. The numbers are spread across the spectrum from red to violet to show their relative size. Zoom in to see the numbers.
%H Scott R. Shannon, <a href="/A361724/a361724_2.png">Image of the first 200000 terms</a>.
%e a(3) = 4 as a(1) + a(2) = 1 + 2 = 3, so a(3) cannot 1,2 or 3. a(3) has a(1) = 1 and a(2) = 2 as neighbors which form sums 4 + 1 = 5 and 4 + 2 = 6 neither of which have appeared, so 4 can be chosen.
%e a(5) = 12 as the numbers already used are 1,2,4,7, which form the sums 3,5,8,6,9,11 with their nearest neighbors. The lowest free number is therefore 10, but a(5) has a(1) = 1 as a neighbor and would create the sum 10 + 1 = 11 which has already appeared as a sum. The next free number is 12 which forms sums 12 + 7 = 19 and 12 + 1 = 13 which have not appeared, so 12 can be chosen.
%Y Cf. A274640, A355270, A358151, A307834, A174344, A274923
%K nonn,look
%O 1,2
%A _Scott R. Shannon_ and _Eric Angelini_, Mar 22 2023
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