OFFSET
1,6
COMMENTS
a(n) is the number of contradictions that are n symbols long in propositional calculus with the connectives not (~), and (*), or (+), implies (->) and if and only if (<->).
When measuring the length of a contradiction, all brackets must be included. The connectives -> and <-> are counted as one symbol each (but writing them as such requires non-ASCII characters).
Formally, the language used for this sequence contains the symbols a-z and A-Z (the variables), ~, *, +, ->, <->, ( and ).
The formulas are defined by the following rules:
- every variable is a formula;
- if A is a formula, then ~A is a formula;
- if A and B are formulas, then (A*B), (A+B), (A->B) and (A<->B) are all formulas.
A formula is a contradiction if it is false for any assignment of truth values to the variables.
LINKS
EXAMPLE
There are 6 contradictions of length 6: ~(a<->a), ~(a->a), (~a*a), (~a<->a), (a*~a) and (a<->~a), so a(6)=6.
There are 2 contradictions of length 7: ~(~a+a) and ~(a+~a), so a(7)=2.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Matthew Scroggs, Oct 08 2016
STATUS
approved