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Minimum sum of a nonnegative integer triple that takes n moves to reach a 0 component, where a move picks two components, subtracts the smaller from the larger, and doubles the smaller.
1

%I #40 Dec 18 2024 19:07:54

%S 0,3,6,11,15,23,27,45,81,105,195,329,597,885,1425,2793,4725,8025,

%T 14265,23205,41685

%N Minimum sum of a nonnegative integer triple that takes n moves to reach a 0 component, where a move picks two components, subtracts the smaller from the larger, and doubles the smaller.

%C a(21) > 65532. - _Karl Desfontaines_, Mar 02 2022

%H IBM's Ponder This, <a href="https://research.ibm.com/haifa/ponderthis/challenges/May2015.html">3 people betting game</a>, May 2015, challenge essentially asks for (a witness for) a(12).

%H Fabian Frei, Peter Rossmanith, and David Wehner, <a href="https://drops.dagstuhl.de/opus/volltexte/2020/12760/pdf/lipics-vol157-fun2021-complete.pdf#page=259">An Open Pouring Problem</a>, 10th International Conference on Fun with Algorithms (FUN 2021). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 14:1-9.

%H John Tromp, <a href="/A256001/a256001.c.txt">C program</a> computing diameter and witness for each sum.

%e The triple (1,2,3) is the triple with minimum sum that has no 0's or equal members and reaches a 0 after the 2 moves (1,2,3) -> (2,2,2) -> (4,0,2). Since the sum of this triple is 6, a(2) = 6.

%o (C) // See link above for a C program from whose output the terms above were derived.

%K nonn,more,changed

%O 0,2

%A _John Tromp_, May 06 2015

%E a(19)-a(20) from _Karl Desfontaines_, Mar 02 2022