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 A354434 #9 May 28 2022 16:37:20 %S A354434 1,2,4,6,3,9,12,18,8,10,14,16,20,22,24,15,21,27,30,33,36,39,26,28,32, %T A354434 34,38,40,42,44,46,48,50,54,45,35,7,63,51,57,60,66,52,72,78,84,56,58, %U A354434 62,64,68,70,74,76,80,82,86,88,90,75,96,100,105,49,77,91,119,102,69,81,108,92,94,98,104 %N A354434 a(1) = 1; for n > 1, a(n) is the smallest unused square spiral number such that a(n) shares a factor with all existing numbers in its Moore neighborhood. %C A354434 The sequence is conjectured to be a permutation of the positive integers, although it takes many terms for most primes to appear, e.g. a(1807) = 13, a(35156) = 179. The primes do not occur in their natural order. In the first 200000 terms the smallest unused prime is 181, while the smallest unused composite number is 11881, which is itself a prime power. %H A354434 Scott R. Shannon, <a href="/A354434/a354434.png">Image of the first 200000 terms</a>. The green line is y = n. %e A354434 The spiral begins %e A354434 . %e A354434 . %e A354434 7--35--45--54--50--48--46 82 %e A354434 | | | %e A354434 63 21--15--24--22--20 44 80 %e A354434 | | | | | %e A354434 51 27 3---6---4 16 42 76 %e A354434 | | | | | | | %e A354434 57 30 9 1---2 14 40 74 %e A354434 | | | | | | %e A354434 60 33 12--18---8--10 38 70 %e A354434 | | | | %e A354434 66 36--39--26--28--32--34 68 %e A354434 | | %e A354434 52--72--78--84--56--58--62--64 %e A354434 . %e A354434 . %e A354434 a(11) = 14 as the existing numbers in the Moore neighborhood when a(11) is being placed are 4,2,8,10, and 14 is the smallest unused number that shares a factor with all these numbers. %Y A354434 Cf. A336946, A064413, A253279, A257112, A257339. %K A354434 nonn,look %O A354434 1,2 %A A354434 _Scott R. Shannon_, May 28 2022