A350627 Solution to Forest of Numbers (Bosque de Números) puzzle if we start with the numbers 1 through n (see Comments).

1, 10, 22, 30, 36, 44

Offset

1,2

Comments

Start with an infinite square grid. Each cell has eight neighbors. Place the numbers 1, 2, ..., n anywhere. Now place the numbers n+1, n+2, ..., m in order, subject to the rule that when you place k, the sum of its neighbors must equal k. Then a(n) is the maximum m that can be achieved.

This is similar to the Stepping Stones problem discussed in A337663, but predates it by more than 20 years.

As can be seen in the El Acertijo (The Riddle) links and in Rodolfo Kurchan's webpage, there are at least six similar problems, for example when the numbers are restricted to an n X n square board. All of these are worthy of inclusion in the OEIS once enough terms are known.

Links

Table of n, a(n) for n=1..6.

El Acertijo, Number 5, Page 8, April 1993.

El Acertijo, Number 5, Page 9, April 1993.

El Acertijo, Number 5, Page 18, April 1993.

El Acertijo, Number 7, Page 15, August/September 1993.

Rudolfo Kurchan, Puzzle Fun

Giorgio Vecchi, Solution for a(5) = 36

Giorgio Vecchi, Solution for a(6) = 44

Crossrefs

Cf. A337663 (Stepping Stones problem).

Sequence in context: A303747 A007366 A302280 * A367918 A109958 A053361

Adjacent sequences: A350624 A350625 A350626 * A350628 A350629 A350630

Keyword

nonn,more

Author

N. J. A. Sloane, Feb 05 2022

Extensions

a(5)-a(6) from Rodolfo Kurchan, Mar 29 2022

Status

approved