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A352621
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a(n) is the minimum possible value of the largest number placed in a solution to the Forest of Numbers (Bosque de Números) puzzle if we start with the numbers 1 and 2 in an n X n grid (see Comments).
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0
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OFFSET
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2,1
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COMMENTS
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Start with an n X n square grid. Each cell has up to eight neighbors. Place the numbers 1 and 2 in any two cells of the grid. Then place a number in each remaining cell, in increasing order (not necessarily using consecutive integers), and with the rule that when you place the number k in a cell, the sum of the numbers in its neighboring cells must equal k. The goal is to fill the grid in such a way as to minimize the largest number placed.
This is similar to the Stepping Stones problem discussed in A337663, but predates it by more than 20 years.
a(7) = 292, a(8) = 502, a(9) = 787 and a(10) 1391 not yet confirmed to be optimal.
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LINKS
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EXAMPLE
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+---+---+---+---+
| 33| 21| 5| 28|
+---+---+---+---+
| 11| 1| 4| 19|
+---+---+---+---+
| 24| 10| 3| 7|
+---+---+---+---+
| 36| 2| 22| 32|
+---+---+---+---+
3 is sum of 1+2, 4=1+3, 5=1+4, 7=3+4, 10=1+2+3+4, 11=1+10, 19=3+4+5+7, 21=1+4+5+11, 22=2+3+7+10.
.
+---+---+---+---+---+
| 32| 18| 63| 30| 56|
+---+---+---+---+---+
| 13| 1| 4| 10| 16|
+---+---+---+---+---+
| 9| 3| 39| 6| 54|
+---+---+---+---+---+
| 36| 5| 2| 8| 14|
+---+---+---+---+---+
| 12| 7| 22| 46| 68|
+---+---+---+---+---+
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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