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A101273 Theorems from propositional calculus, translated into decimal digits. 5


%S 171,181,272,282,1531,1631,2532,2632,3151,3161,3252,3262,11711,11811,

%T 12712,12812,14171,14181,14271,14272,15171,15172,16171,16181,17141,

%U 17161,17162,17261,17331,17910,18141,18161,18331,18910,21721,21821,22722,22822,24171

%N Theorems from propositional calculus, translated into decimal digits.

%C 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.

%C Operator binding strength is in numerical order, Not > And > ... > Equiv.

%C The non-associative "Implies" is evaluated from Left to Right; A->B->C = is interpreted (A->B)->C. Redundant parentheses are permitted.

%C 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_, Dec 19 2004

%D Davis, M., Computability and Unsolvability. New York: Dover 1982.

%D Hofstadter, D. R., Goedel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, p. 18, 1989.

%D Kleene, S. C., Mathematical Logic. New York: Dover, 2002.

%H Charles R Greathouse IV, <a href="/A101273/b101273.txt">Table of n, a(n) for n=1..10000</a>

%H Eric Weisstein et al., <a href="http://mathworld.wolfram.com/GoedelNumber.html">"Goedel Number."</a>

%F It appears that the n-th term is very roughly n^c, for some c>1.

%e Example: 17162 is the theorem A->AvB.

%K nonn,base

%O 1,1

%A Richard C. Schroeppel, Dec 19 2004

%E Corrected and edited by _Charles R Greathouse IV_, Oct 06 2009

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Last modified December 16 07:12 EST 2018. Contains 318158 sequences. (Running on oeis4.)