This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A361724 #13 Mar 22 2023 08:06:27 %S A361724 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 A361724 82,70,89,94,83,48,62,105,100,69,117,25,111,129,127,124,143,106,112, %U A361724 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 A361724 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 A361724 Scott R. Shannon, <a href="/A361724/a361724_1.png">Image of the first 50000 terms</a>. The green line is a(n) = n. %H A361724 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 A361724 Scott R. Shannon, <a href="/A361724/a361724_2.png">Image of the first 200000 terms</a>. %e A361724 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 A361724 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 A361724 Cf. A274640, A355270, A358151, A307834, A174344, A274923 %K A361724 nonn,look %O A361724 1,2 %A A361724 _Scott R. Shannon_ and _Eric Angelini_, Mar 22 2023