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A352621 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). 0
6, 12, 36, 68, 140 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
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.
Computer solutions by Dmitry Kamenetsky.
a(7) = 292, a(8) = 502, a(9) = 787 and a(10) 1391 not yet confirmed to be optimal.
LINKS
EXAMPLE
4 X 4 = 36 solution by Rodolfo Kurchan:
+---+---+---+---+
| 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.
.
5 X 5 = 68 solution by Dmitry Kamenetsky:
+---+---+---+---+---+
| 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|
+---+---+---+---+---+
CROSSREFS
Sequence in context: A306899 A096932 A212976 * A176681 A064476 A324483
KEYWORD
nonn,more
AUTHOR
Rodolfo Kurchan, Mar 24 2022
STATUS
approved

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Last modified June 15 11:51 EDT 2024. Contains 373407 sequences. (Running on oeis4.)