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 A332755 #16 Oct 30 2022 15:09:09 %S A332755 1,1,1,1,2,2,3,4,6,8,12,16,23,31,45,61,87,119,171,233,334,459,655,904, %T A332755 1288,1782,2535,3517,4995,6935,9848,13703,19437,27070,38376,53528, %U A332755 75842,105878,149966,209555,296707,414922,587304,821853,1163052,1628574,2304082 %N A332755 Lapidary numbers. %C A332755 Consider a two-player stone-throwing game with a single shared pile of stones. The players alternately remove one or more stones from the pile until it is empty. In addition, each player seeks to communicate a message through their sequence of moves. If there are initially n stones then a(n) is the largest number m such that both players can communicate at least m distinct messages. %C A332755 For n > 0, a(n) is also the size of the Durfee square of the partition defined in A064660. %H A332755 Peter J. Taylor, <a href="/A332755/b332755.txt">Table of n, a(n) for n = 0..60</a> %H A332755 Peter J. Taylor, <a href="http://www.cheddarmonk.org/papers/lapidary.pdf">The lapidary numbers, or the combinatorics of communication by throwing stones</a> (preprint). %H A332755 Peter J. Taylor, <a href="https://archim.org.uk/eureka/archive/Eureka-65.pdf">The lapidary numbers, or the combinatorics of communication by throwing stones</a>, Eureka, 65 (2018), pp. 89-90. %H A332755 Peter J. Taylor, <a href="/A332755/a332755.py.txt">Python program</a> %F A332755 Asymptotically, a(n) is within a subexponential factor of 2^(n/2). %e A332755 For n=4, one strategy which allows both players to communicate one of two messages is each remove one or two stones on their first turn. %Y A332755 Cf. A064660. %K A332755 nonn %O A332755 0,5 %A A332755 _Peter J. Taylor_, Feb 22 2020