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 A340000 #28 Jan 10 2021 22:25:29 %S A340000 1,17,33,46 %N A340000 Solution to stacking stones puzzle (see Comments). %C A340000 This is a variant of the stepping stone puzzle sequence (A337663), where you start by placing n 1's on an infinite square grid. Then place the numbers 2,3,... in order on the grid, following the rule that the sum of the 8 surrounding cells has to be equal to the number placed on a cell. a(n) is the largest number which can be achieved starting with n 1's. Additionally, there are 2 different new rules in this "stacking stones" sequence: %C A340000 1. You can "stack" numbers on top of already placed numbers when the sum of the surrounding 8 cells is equal to the new number. The number inside the cell is not added to the sum and is replaced as value of the cell with the new number. %C A340000 2. The starting 1's have to be at least one cell apart (to avoid a trivial infinite solution). %H A340000 S. Brunner, <a href="/A340000/a340000.txt">Python program</a> %e A340000 Illustration for a(3)=33: %e A340000 +------+------+------+------+------+------+------+ %e A340000 | | | | | | | | %e A340000 | | | 18 | 17 | 26 | | 33 | %e A340000 | | | | [4] | [13] | | | %e A340000 +------+------+------+------+------+------+------+ %e A340000 | | | | | | | | %e A340000 | | | | 1 | 3 | 5 | 28 | %e A340000 | | | | | | | | %e A340000 +------+------+------+------+------+------+------+ %e A340000 | | | | | | | | %e A340000 | | 21 | 14 | 27 | 2 | 23 | | %e A340000 | | | | [6] | | [11] | | %e A340000 +------+------+------+------+------+------+------+ %e A340000 | | | | | | | | %e A340000 | 22 | | 7 | | | 1 | 24 | %e A340000 | | | | | | | [12] | %e A340000 +------+------+------+------+------+------+------+ %e A340000 | | | | | | | | %e A340000 | | 1 | 8 | 31 | 32 | | 25 | %e A340000 | | | | [15] | [16] | | | %e A340000 +------+------+------+------+------+------+------+ %e A340000 | 30 | 29 | | | | | | %e A340000 | [20] | [19] | | | | | | %e A340000 | [10] | [9] | | | | | | %e A340000 +------+------+------+------+------+------+------+ %e A340000 Illustration for a(4)=46: %e A340000 +------+------+------+------+------+------+------+------+------+------+------+------+ %e A340000 | | | | | | | | | | | | | %e A340000 | 32 | | 37 | 44 | | | | | | | | | %e A340000 | | | [15] | [22] | | | | | | | | | %e A340000 +------+------+------+------+------+------+------+------+------+------+------+------+ %e A340000 | | | | | | | | | | | | | %e A340000 | 24 | 8 | 7 | | | 39 | | | | 42 | | 29 | %e A340000 | | | | | | | | | | | | | %e A340000 +------+------+------+------+------+------+------+------+------+------+------+------+ %e A340000 | | | | 31 | | | | | | | | | %e A340000 | | 16 | 1 | [13] | 18 | 21 | | | | 41 | 1 | 28 | %e A340000 | | | | [6] | | | | | | | | | %e A340000 +------+------+------+------+------+------+------+------+------+------+------+------+ %e A340000 | | | | | | | | | | | | | %e A340000 | | 17 | | 2 | 3 | | | 43 | | 40 | | 27 | %e A340000 | | | | | | | | | | [14] | | | %e A340000 +------+------+------+------+------+------+------+------+------+------+------+------+ %e A340000 | | | | | | | | | | | | | %e A340000 | | 36 | 19 | | 34 | 4 | 9 | 33 | 1 | 12 | 26 | | %e A340000 | | | | | [1] | | | [10] | | | | | %e A340000 +------+------+------+------+------+------+------+------+------+------+------+------+ %e A340000 | | | | | | | | | 46 | | | | %e A340000 | | | | 20 | | 5 | | | [23] | | 38 | | %e A340000 | | | | | | | | | [11] | | | | %e A340000 +------+------+------+------+------+------+------+------+------+------+------+------+ %e A340000 | | | | | | | | | | | | | %e A340000 | | | | 45 | 25 | 30 | 35 | | | | | | %e A340000 | | | | | | | | | | | | | %e A340000 +------+------+------+------+------+------+------+------+------+------+------+------+ %Y A340000 Cf. A337663. %K A340000 nonn,more,hard %O A340000 1,2 %A A340000 _S. Brunner_, Dec 26 2020