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 A332755 Lapidary numbers. 1
 1, 1, 1, 1, 2, 2, 3, 4, 6, 8, 12, 16, 23, 31, 45, 61, 87, 119, 171, 233, 334, 459, 655, 904, 1288, 1782, 2535, 3517, 4995, 6935, 9848, 13703, 19437, 27070, 38376, 53528, 75842, 105878, 149966, 209555, 296707, 414922, 587304, 821853, 1163052, 1628574, 2304082 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS 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. For n > 0, a(n) is also the size of the Durfee square of the partition defined in A064660. REFERENCES Peter J. Taylor, The lapidary numbers, or the combinatorics of communication by throwing stones, Eureka, 65 (2018), pp89-90. LINKS Peter J. Taylor, Table of n, a(n) for n = 0..60 Peter J. Taylor, The lapidary numbers, or the combinatorics of communication by throwing stones (preprint) Peter J. Taylor, Python program FORMULA Asymptotically, a(n) is within a subexponential factor of 2^(n/2). EXAMPLE 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. CROSSREFS Cf. A064660. Sequence in context: A318403 A334626 A339235 * A017912 A102543 A173383 Adjacent sequences:  A332752 A332753 A332754 * A332756 A332757 A332758 KEYWORD nonn AUTHOR Peter J. Taylor, Feb 22 2020 STATUS approved

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Last modified June 29 18:25 EDT 2022. Contains 354913 sequences. (Running on oeis4.)