%I A113497
%S A113497 1,3,6,6,11,9,16,12,21,15,26,18,31,21,36,24,41,27,46,30,51,33,56,36,61,
%T A113497 39,66,42,71,45,76,48,81,51,86,54,91,57,96
%N A113497 Ascending descending base exponent transform of a simple periodic sequence 
               (A000034).
%C A113497 A000034 = 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 
               1, ... = continued fraction for (sqrt(3)+1)/2 (cf. A040001) = base 
               3 digital root of n+1. In general, the ascending descending base 
               exponent transform of any simple periodic sequence can be written 
               as a periodic set of interleaved sequences.
%F A113497 a(n) = SUM[from i = 1 to n] (A000034(i))^(A000034(n-i+1)). a(2n) = 3n. 
               a(2n+1) = 5n+1.
%e A113497 a(1) = 1^1 = 1.
%e A113497 a(2) = 1^2 + 2^1 = 3.
%e A113497 a(3) = 1^1 + 2^2 + 1^1 = 6.
%e A113497 a(4) = 1^2 + 2^1 + 1^2 + 2^1 = 6.
%e A113497 a(5) = 1^1 + 2^2 + 1^1 + 2^2 + 1^1 = 11.
%e A113497 a(6) = 1^2 + 2^1 + 1^2 + 2^1 + 1^2 + 2^1 = 9.
%Y A113497 Cf. A000034, A113320, A005408, A113122, A113153, A113154, A113336, A113271, 
               A113258, A113257, A113231, A087316, A113208.
%Y A113497 Sequence in context: A002853 A135610 A157018 this_sequence A158662 A119980 
               A066779
%Y A113497 Adjacent sequences: A113494 A113495 A113496 this_sequence A113498 A113499 
               A113500
%K A113497 easy,nonn
%O A113497 1,2
%A A113497 Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 10 2006