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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)
 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 M. Scroggs, Logical Contradictions M. Scroggs, List of contradictions 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 Cf. A256120, A277276. Sequence in context: A081778 A055943 A319313 * A213503 A169632 A201445 Adjacent sequences:  A277272 A277273 A277274 * A277276 A277277 A277278 KEYWORD nonn,more AUTHOR Matthew Scroggs, Oct 08 2016 STATUS approved

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Last modified August 21 06:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)