%I A113533
%S A113533 1,3,4,5,7,12,10,15,14,14,23,16,20,27,21,30,27,25,40,28
%N A113533 Ascending descending base exponent transform of the infinite Fibonacci 
               word (A003842).
%C A113533 The infinite Fibonacci word b(n) is the fixed point of the morphism 1->
               12, 2->1, starting from b(1) = 2. This transform a(n) of that sequence 
               b(n) satisfies n =< a(n) =< 4*n, but that is not a tight bound.
%e A113533 a(1) = A003842(1)^A003842(1) = 1^1 = 1.
%e A113533 a(2) = A003842(1)^A003842(2) + A003842(2)^A003842(1) = 1^2 + 2^1 = 3.
%e A113533 a(3) = 1^1 + 2^2 + 1^1 = 4.
%e A113533 a(4) = 1^1 + 2^1 + 1^2 + 1^1 = 5.
%e A113533 a(5) = 1^2 + 2^1 + 1^1 + 1^2 + 2^1 = 7.
%e A113533 a(6) = 1^1 + 2^2 + 1^1 + 1^1 + 2^2 + 1^1 = 12.
%e A113533 a(7) = 1^2 + 2^1 + 1^2 + 1^1 + 2^1 + 1^2 + 2^1 = 10.
%e A113533 a(8) = 1^1 + 2^2 + 1^1 + 1^2 + 2^1 + 1^1 + 2^2 + 1^1 = 15.
%e A113533 a(9) = 1^1 + 2^1 + 1^2 + 1^1 + 2^2 + 1^1 + 2^1 + 1^2 + 1^1 = 14.
%e A113533 a(10) = 1^2 + 2^1 + 1^1 + 1^2 + 2^1 + 1^2 + 2^1 + 1^1 + 1^2 + 2^1 = 14.
%Y A113533 Cf. A003842, A113320, A005408, A113122, A113153, A113154, A113336, A113271, 
               A113258, A113257, A113231, A087316, A113208, A113498.
%Y A113533 Sequence in context: A137950 A046413 A120635 this_sequence A023713 A032890 
               A092859
%Y A113533 Adjacent sequences: A113530 A113531 A113532 this_sequence A113534 A113535 
               A113536
%K A113533 easy,nonn
%O A113533 1,2
%A A113533 Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 13 2006