A003039 Maximal number of prime implicants of a Boolean function of n variables. (Formerly M1596)

1, 2, 6, 13, 32, 92

Offset

1,2

Comments

Dunham and Fridsal showed that a(8) is at least 576. - Don Knuth, Aug 25 2005

References

M. M. Gadzhiev, Maximal length of the reduced disjunctive normal form for Boolean functions with five and six variables, Diskretnyi Analiz (Novosibirsk), (1971), 3-24 [ Computing Reviews #23,815, Sep. 1972 ].

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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

B. Dunham and R. Fridshal, The problem of simplifying logical expressions, Journal of Symbolic Logic, 24 (1959), 17-19.

M. M. Gadzhiev, Maximal length of the reduced disjunctive normal form for Boolean functions with five and six variables, Diskretnyi Analiz (Novosibirsk), (1971), 3-24 [ Computing Reviews #23,815, Sep. 1972 ]. [Annotated scanned copy]

M. M. Gadzhiev, Maximal length of the reduced disjunctive normal form for Boolean functions with five and six variables (abstract), Diskretnyi Analiz (Novosibirsk), (1971), 3-24 [ Computing Reviews #23,815, Sep. 1972 ]. [Annotated scanned copy of abstract]

Index entries for sequences related to Boolean functions

Example

a(3)=6 because of (x XOR y) OR (x XOR z) OR (y XOR z).

Crossrefs

Sequence in context: A099232 A280758 A053562 * A109385 A244578 A238827

Adjacent sequences: A003036 A003037 A003038 * A003040 A003041 A003042

Keyword

nonn,hard,more,nice

Author

N. J. A. Sloane

Status

approved