

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




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.
a(7) = 292, a(8) = 502, a(9) = 787 and a(10) 1391 not yet confirmed to be optimal.


LINKS



EXAMPLE

+++++
 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
++++++


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



