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A277275 Number of contradictions in propositional calculus of length n. 2
0, 0, 0, 0, 0, 6, 2, 20, 6, 127, 154 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..11.

M. Scroggs, Logical Contradictions

M. Scroggs, List of contradictions


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.


Cf. A256120, A277276.

Sequence in context: A081778 A055943 A319313 * A213503 A169632 A201445

Adjacent sequences:  A277272 A277273 A277274 * A277276 A277277 A277278




Matthew Scroggs, Oct 08 2016



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Last modified July 14 00:36 EDT 2020. Contains 335716 sequences. (Running on oeis4.)