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 A345440 #35 May 29 2022 17:59:55
%S A345440 0,1,3,2,3,1,3,2,3,6,4,6,12,9,8,9,12,6,4,6,12,9,8,9,12,17,11,9,11,17,
%T A345440 27,22,19,18,19,22,27,17,11,9,11,17,27,22,19,18,19,22,27,34,24,18,16,
%U A345440 18,24,34,48,41,36,33,32,33,36,41,48,34,24,18,16,18,24
%N A345440 Represent the ring R = {x+y*sqrt(-2): x, y rational integers} by the cells centered at the points (x,y) of a square grid, as in A345437; number the cells of the grid along a counterclockwise square spiral, with the cells at (0,0) and (1,0) numbered 0, 1; then a(n) is the norm x^2+2*y^2 of the element of R occupying the n-th cell.
%H A345440 Rémy Sigrist, <a href="/A345440/b345440.txt">Table of n, a(n) for n = 0..10000</a>
%H A345440 Rémy Sigrist, <a href="/A345440/a345440.gp.txt">PARI program for A345440</a>
%H A345440 N. J. A. Sloane, <a href="/A345437/a345437.pdf">Illustration of initial terms</a> [An enlargement of Figure 3 of Wichmann (2019), showing the numbering of the initial cells of the square spiral. The origin is black, the two units +-1 are red, and the primes are blue.]
%H A345440 N. J. A. Sloane, <a href="/A345440/a345440.pdf">Illustration of initial terms.</a> [The cell numbers are black, their norms are red.]
%H A345440 Brian Wichmann, <a href="http://www.tilingsearch.org/special/ufd.pdf">Tiling for Unique Factorization Domains</a>, Jul 22 2019.
%F A345440 a(n) = A174344(n+1)^2 + 2*A274923(n+1)^2. - _Rémy Sigrist_, Jun 26 2021
%o A345440 (PARI) See Links section.
%Y A345440 Cf. A174344, A274923, A336336, A345435, A345437, A345439.
%K A345440 nonn
%O A345440 0,3
%A A345440 _N. J. A. Sloane_, Jun 25 2021
%E A345440 More terms from _Rémy Sigrist_, Jun 26 2021