%I A113534
%S A113534 1,3,4,7,20,10,39,12,26,19,20,43
%N A113534 Ascending descending base exponent transform of the flipped tribonacci 
               substitution (A092782).
%C A113534 The flipped tribonacci substitution (A092782) b(n) is the fixed point 
               of the morphism 1 -> 12, 2 -> 13, 3 -> 1, starting from b(1) = 1. 
               The transformed sequence a(n) satisfies n =< a(n) =< 27 n but the 
               bound can be determined to be much tighter.
%D A113534 V. F. Sirvent, Semigroups and the self-similar structure of the flipped 
               tribonacci substitution, Applied Math. Letters, 12 (1999), 25-29. 
               [Contains many further references.]
%e A113534 a(1) = A092782(1)^A092782(1) = 1^1 = 1.
%e A113534 a(2) = A092782(1)^A092782(2) + A092782(2)^A092782(1) = 1^2 + 2^1 = 3.
%e A113534 a(3) = 1^1 + 2^2 + 1^1 = 4.
%e A113534 a(4) = 1^3 + 2^1 + 1^2 + 3^1 = 7.
%e A113534 a(5) = 1^1 + 2^3 + 1^1 + 3^2 + 1^1 = 20.
%e A113534 a(6) = 1^2 + 2^1 + 1^3 + 3^1 + 1^2 + 2^1 = 10.
%e A113534 a(7) = 1^1 + 2^2 + 1^1 + 3^3 + 1^1 + 2^2 + 1^1 = 39.
%e A113534 a(8) = 1^1 + 2^1 + 1^2 + 3^1 + 1^3 + 2^1 + 1^2 + 1^1 = 12.
%e A113534 a(9) = 1^2 + 2^1 + 1^1 + 3^2 + 1^1 + 2^3 + 1^1 + 1^2 + 2^1 = 26.
%e A113534 a(10) = 1^1 + 2^2 + 1^1 + 3^1 + 1^2 + 2^1 + 1^3 + 1^1 + 2^2 + 1^1 = 19.
%e A113534 a(11) = 1^3 + 2^1 + 1^2 + 3^1 + 1^1 + 2^2 + 1^1 + 1^3 + 2^1 + 1^2 + 3^1 
               = 20.
%e A113534 a(12) = 1^1 + 2^3 + 1^1 + 3^2 + 1^1 + 2^1 + 1^2 + 1^1 + 2^3 + 1^1 + 3^2 
               + 1^1 = 43.
%Y A113534 Cf. A092782, A113320, A005408, A113122, A113153, A113154, A113336, A113271, 
               A113258, A113257, A113231, A087316, A113208, A113498.
%Y A113534 Sequence in context: A041497 A042227 A117789 this_sequence A030724 A124082 
               A056655
%Y A113534 Adjacent sequences: A113531 A113532 A113533 this_sequence A113535 A113536 
               A113537
%K A113534 easy,nonn
%O A113534 1,2
%A A113534 Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 13 2006