Search: id:A101273
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%I A101273
%S A101273 171,181,272,282,1531,1631,2532,2632,2711,2811,3151,3161,3252,3262,
%T A101273 11712,11721,11812,11821,12722,12822,14171,14181,14271,14272,15171,
%U A101273 15172,16171,16181,17141,17161,17162,17261,17331,17910,18141,18161
%N A101273 Theorems from propositional calculus, translated into decimal digits.
%C A101273 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 A101273 Operator binding strength is in numerical order, Not > And > ... > Equiv.
%C A101273 The non-associative "Implies" is evaluated from Left to Right; A->B->
               C = is interpreted (A->B)->C. Redundant parentheses are permitted.
%C A101273 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
%D A101273 Davis, M., Computability and Unsolvability. New York: Dover 1982.
%D A101273 Hofstadter, D. R., Goedel, Escher, Bach: An Eternal Golden Braid. New 
               York: Vintage Books, p. 18, 1989.
%D A101273 Kleene S. C., Mathematical Logic. New York: Dover, 2002.
%H A101273 Charles R Greathouse IV, <a href="b101273.txt">Table of n, a(n) for n=1..10000</
               a>
%H A101273 Eric Weisstein et al., <a href="http://mathworld.wolfram.com/GoedelNumber.html">
               "Goedel Number."</a>
%F A101273 It appears that the n-th term is very roughly n^c, for some c>1.
%e A101273 Example: 17162 is the theorem A->AvB.
%Y A101273 Sequence in context: A015975 A045149 A031511 this_sequence A136365 A031900 
               A120819
%Y A101273 Adjacent sequences: A101270 A101271 A101272 this_sequence A101274 A101275 
               A101276
%K A101273 nonn
%O A101273 1,1
%A A101273 Richard Schroeppel (rschroe(AT)sandia.gov), Dec 19 2004
%E A101273 Corrected and edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), 
               Oct 06 2009

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