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A271863 Recursive sequence based on the central polygonal numbers (A000124) and A004736.

%I A271863 #13 Apr 19 2016 02:36:58
%S A271863 1,2,4,3,8,6,7,10,12,5,11,19,16,14,18,15,22,25,17,9,24,13,29,23,32,28,
%T A271863 26,31,27,39,20,38,40,33,35,30,34,49,36,46,37,21,45,43,48,44,51,59,41,
%U A271863 56,42,50,55,53,58,54,67,62,70,64,57,65,63,52,60,69,47
%N A271863 Recursive sequence based on the central polygonal numbers (A000124) and A004736.
%C A271863 Conjectured to be a permutation of the natural numbers.
%C A271863 The central polygonal numbers can be constructed by starting with the natural numbers, setting A000124(0)=1 and obtaining A000124(n+1) by reversing the order of the next A000124(n) numbers after A000124(n). This procedure doesn't produce a permutation of the natural numbers for A000124 because the sequence is strictly increasing. The present sequence is constructed by the same procedure, except that a(n+1) is obtained by reversing the next a(A004736(n)) numbers.
%H A271863 Max Barrentine, <a href="/A271863/b271863.txt">Table of n, a(n) for n = 1..1082</a>
%e A271863 Start with the natural numbers:
%e A271863 1, 2, 3, 4, 5, 6, 7, 8...
%e A271863 a(A004736(1))=1, so reverse the order of the next term, leaving the sequence unchanged:
%e A271863    (1)
%e A271863 1, (2), 3, 4, 5, 6, 7, 8...
%e A271863 a(A004736(2))=2, so reverse the order of the next 2 terms:
%e A271863       (2)
%e A271863 1, 2, (4, 3), 5, 6, 7, 8, 9...
%e A271863 a(A004736(3))=1, so reverse the order of the next term, leaving the sequence unchanged:
%e A271863          (1)
%e A271863 1, 2, 4, (3), 5, 6, 7, 8...
%e A271863 a(A004736(4))=4, so reverse the order of the next 4 terms:
%e A271863             (4)
%e A271863 1, 2, 4, 3, (8, 7, 6, 5)...
%e A271863 a(A004736(5))=2, so reverse the order of the next 2 terms:
%e A271863                (2)
%e A271863 1, 2, 4, 3, 8, (6, 7), 5...
%e A271863 a(A004736(6))=1, so reverse the order of the next term, leaving the sequence unchanged:
%e A271863                   (1)
%e A271863 1, 2, 4, 3, 8, 6, (7), 5...
%Y A271863 Cf. A000124, A004736.
%K A271863 nonn
%O A271863 1,2
%A A271863 _Max Barrentine_, Apr 15 2016