login
Numbers n such that there are a prime number of unlabeled distributive lattices with n elements.
0

%I #5 Mar 30 2012 18:40:58

%S 4,5,6,10,12,13,18,21,23,26

%N Numbers n such that there are a prime number of unlabeled distributive lattices with n elements.

%C A lattice which satisfies the identities:

%C (x^y)V(x^z) = x^(yVz);

%C (xVy)^(xVz) = xV(y^z)

%C is said to be distributive.

%D Gratzer, G. Lattice Theory: First Concepts and Distributive Lattices. San Francisco, CA: W. H. Freeman, pp. 35-36, 1971.

%F {k: A006982(k) is in A000040}.

%e a(10) = 26 because there are 711811 unlabeled distributive lattices with 26 elements, and 711811 is a prime number.

%Y Cf. A000040, A006982

%K nonn

%O 1,1

%A _Jonathan Vos Post_, Feb 26 2011