A109943 Maximal number of distinct primes in the solution of the n X n generalization of the Gordon Lee puzzle.

1, 11, 30, 63, 116, 187, 281

Offset

1,2

Comments

The Gordon Lee puzzle asks for an n X n array of single digits such that as many distinct primes as possible are formed by joining consecutive digits in any horizontal, vertical or diagonal direction, forward or backward. a(4)=63 was proved in March 2005 by Mike Oakes. a(5) and a(6) are conjectured best values that resisted any improvement since 1998.

a(5), a(6) and a(7) are conjectured best values that have resisted any improvement since 1998, including the joint effort of more than 100 participants in a programming contest in summer 2005. The best currently (September 2005) known lower bounds for the next terms are a(8)>=394 and a(9)>=527. - Hugo Pfoertner, Sep 21 2005

Links

Table of n, a(n) for n=1..7.

Carlos Rivera, The Gordon Lee puzzle.

Carlos Rivera, Best Solutions

Eric Weisstein's World of Mathematics, Prime Array.

Al Zimmermann's Programming Contests. Primal Squares: Best grids for part 1 found during the contest.

Crossrefs

Cf. A032529 = all primes in the 3 X 3 record matrix, A034720 = number of candidates to be checked for primality in an n X n matrix of single digits.

A111128 gives the solutions to Part 2 of the contest.

Sequence in context: A163060 A247433 A051682 * A303856 A137411 A002755

Adjacent sequences: A109940 A109941 A109942 * A109944 A109945 A109946

Keyword

hard,more,nonn

Author

Hugo Pfoertner, Jul 05 2005

Extensions

a(7) from Hugo Pfoertner, Sep 21 2005

Status

approved