login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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