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Search: id:A101273
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| A101273 |
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Theorems from propositional calculus, translated into decimal digits. |
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+0
5
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| 171, 181, 272, 282, 1531, 1631, 2532, 2632, 2711, 2811, 3151, 3161, 3252, 3262, 11712, 11721, 11812, 11821, 12722, 12822, 14171, 14181, 14271, 14272, 15171, 15172, 16171, 16181, 17141, 17161, 17162, 17261, 17331, 17910, 18141, 18161
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Blocks of 1s and 2s are variables: A = 1, B = 2, C = 11, D = 12, E = 21, ... Not = 3; And = 4; Xor = 5; Or = 6; Implies = 7; Equiv = 8; Left Parenthesis = 9; Right Parenthesis = 0.
Operator binding strength is in numerical order, Not > And > ... > Equiv.
The non-associative "Implies" is evaluated from Left to Right; A->B->C = is interpreted (A->B)->C. Redundant parentheses are permitted.
This is a decimal Goedelization of theorems from a particular axiomatization of propositional calculus. This should be linked to the subsequences of theorems and antitheorems. - Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 19 2004
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REFERENCES
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Davis, M., Computability and Unsolvability. New York: Dover 1982.
Hofstadter, D. R., Goedel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, p. 18, 1989.
Kleene S. C., Mathematical Logic. New York: Dover, 2002.
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n=1..10000
Eric Weisstein et al., "Goedel Number."
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FORMULA
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It appears that the n-th term is very roughly n^c, for some c>1.
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EXAMPLE
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Example: 17162 is the theorem A->AvB.
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CROSSREFS
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Sequence in context: A015975 A045149 A031511 this_sequence A136365 A031900 A120819
Adjacent sequences: A101270 A101271 A101272 this_sequence A101274 A101275 A101276
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KEYWORD
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nonn
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AUTHOR
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Richard Schroeppel (rschroe(AT)sandia.gov), Dec 19 2004
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EXTENSIONS
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Corrected and edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 06 2009
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