%I A098281
%S A098281 1,1,2,2,1,1,2,3,1,3,2,3,1,2,2,1,3,2,3,1,3,2,1,1,2,3,4,1,2,4,3,1,4,2,3,
%T A098281 4,1,2,3,1,3,2,4,1,3,4,2,1,4,3,2,4,1,3,2,3,1,2,4,3,1,4,2,3,4,1,2,4,3,1,
%U A098281 2,2,1,3,4,2,1,4,3,2,4,1,3,4,2,1,3,2,3,1,4,2,3,4,1,2,4,3,1,4,2,3,1,3,2
%N A098281 Back-to-front insertion-permutation sequence; contains every finite sequence 
               of distinct positive integers.
%C A098281 Contains every finite sequence of distinct numbers...infinitely many 
               times.
%F A098281 Write 1. Then place 2 after 1 and then 2 before 1, yielding 12 and 21, 
               as well as the first 5 terms of the sequence. Next, generate the 
               6 permutations of 1, 2, 3 by inserting 3 into 12 and then 21, from 
               back-to-front, like this: 123, 132, 312 then 213, 231, 321. Next, 
               generate the 24 permutations of 1, 2, 3, 4 by inserting 4 into the 
               permutations of 1, 2, 3. Continue forever.
%e A098281 The permutations can be written as
%e A098281 1,
%e A098281 12, 21,
%e A098281 123, 132, 312, 213, 231, 321, etc.
%e A098281 Write them in order and insert commas.
%Y A098281 Cf. A098280, A030298.
%Y A098281 Sequence in context: A016533 A122915 A030298 this_sequence A103343 A085263 
               A115092
%Y A098281 Adjacent sequences: A098278 A098279 A098280 this_sequence A098282 A098283 
               A098284
%K A098281 nonn
%O A098281 1,3
%A A098281 Clark Kimberling (ck6(AT)evansville.edu), Sep 01 2004