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 A341363 #37 Feb 14 2021 13:18:04 %S A341363 1,2,10,3,48,45,4,60,276,136,5,68,321,928,325,6,80,368,1040,2349,666, %T A341363 7,92,384,1168,2575,4984,1225,8,100,429,1296,2825,5382,9391,2080,9, %U A341363 124,456,1388,3075,5816,10030,16228,3321,10,128,554,1656,3627,6250,10718,17190,26257,5050 %N A341363 Table read by antidiagonals: T(n, k) is the sum of the numbers inside the k-th square of size n X n when the square spiral is tiled with these squares, where each tile contains numbers which sum to the minimum possible value, and each number on the spiral can only be in one tile. %C A341363 The terms for a given n tend to have larger jumps in value at one more than the square of the odd numbers, i.e., at k = (2*t+1)^2 + 1, t >= 0, due to the previous square filling a grid of squares containing (2*t+1)^2 squares. This forces the next square to move further away from the origin and into spiral arms containing larger numbers. %C A341363 See A341278 for the smallest spiral number not covered by any square in each n X n tiling. %H A341363 Scott R. Shannon, <a href="/A341363/a341363_5.png">Image for n=2, k = 1..2000</a>. The image can be zoomed in to see the numbers of the square spiral. In this and other images the colors are graduated around the spectrum to show the squares relative placement order. %H A341363 Scott R. Shannon, <a href="/A341363/a341363_6.png">Image for n=4, k = 1..1000</a>. %H A341363 Scott R. Shannon, <a href="/A341363/a341363_7.png">Image for n=5, k = 1..1000</a>. %H A341363 Scott R. Shannon, <a href="/A341363/a341363_8.png">Image for n=7, k = 1..1000</a>. %H A341363 Scott R. Shannon, <a href="/A341363/a341363_9.png">Image for n=10, k = 1..500</a>. %F A341363 T(1,k) = k. %F A341363 T(n,1) = n^2*(n^2+1)/2 = A000217(n^2). %e A341363 The table begins: %e A341363 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... %e A341363 10, 48, 60, 68, 80, 92, 100, 124, 128, 156, ... %e A341363 45, 276, 321, 368, 384, 429, 456, 554, 702, 803, ... %e A341363 136, 928, 1040, 1168, 1296, 1388, 1656, 1696, 1858, 2876, ... %e A341363 325, 2349, 2575, 2825, 3075, 3627, 3935, 4243, 4415, 7740, ... %e A341363 666, 4984, 5382, 5816, 6250, 8456, 9188, 9576, 10154, 14204, ... %e A341363 1225, 9391, 10030, 10718, 11406, 15006, 16260, 16737, 17627, 27701, ... %e A341363 2080, 16228, 17190, 18216, 19242, 24856, 26856, 27392, 28692, 49240, ... %e A341363 3321, 26257, 27636, 29096, 30556, 38998, 42010, 42561, 44383, 81527, ... %e A341363 5050, 40344, 42246, 44248, 46250, 58560, 62892, 63400, 65870, 127660, ... %e A341363 7381, 59459, 62002, 64666, 67330, 84806, 90808, 91201, 94459, 191129, ... %e A341363 ... %e A341363 . %e A341363 a(2,1) = 10 as the first square of size 2 X 2 is placed such that it covers the numbers 1,2,3,4, which sum to 10. This is the minimum possible sum. %e A341363 a(2,2) = 48 as the second square of size 2 X 2 is placed such that it covers the numbers 5,6,18,19, which sum to 48. This is the minimum possible sum for such a square which does not use the previously covered numbers 1,2,3,4. %e A341363 a(2,3) = 60 as the third square of size 2 X 2 is placed such that it covers the numbers 7,8,22,23, which sum to 60. This is the minimum possible sum for such a square which does not use the previously covered numbers 1,2,3,4,5,6,18,19. %Y A341363 Cf. A341160, A341327, A340974, A174344, A274923, A296030, A275161. %K A341363 nonn,tabl %O A341363 1,2 %A A341363 _Scott R. Shannon_, Feb 10 2021