A271861 Recursive sequence based on the central polygonal numbers (A000124) and A002260.

1, 2, 3, 5, 4, 7, 9, 8, 10, 12, 15, 14, 6, 16, 19, 11, 13, 18, 21, 24, 20, 28, 27, 25, 22, 30, 23, 34, 37, 36, 26, 29, 33, 17, 41, 44, 40, 39, 32, 35, 45, 31, 49, 52, 48, 55, 54, 51, 38, 46, 50, 58, 61, 57, 64, 67, 66, 56, 43, 59, 47, 68, 71, 63, 74, 77, 81

Offset: 1

Author

Max Barrentine, Apr 15 2016

Keywords

• nonn

Comments

Conjectured to be a permutation of the natural numbers.

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(A002260(n)) numbers.

Examples

			Start with the natural numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9...
a(A002260(1))=1, so reverse the order of the next term, leaving the sequence unchanged:
   (1)
1, (2), 3, 4, 5, 6, 7, 8, 9...
a(A002260(2))=1, so reverse the order of the next term, leaving the sequence unchanged:
      (1)
1, 2, (3), 4, 5, 6, 7, 8, 9...
a(A002260(3))=2, so reverse the order of the next 2 terms:
         (2)
1, 2, 3, (5, 4), 6, 7, 8, 9...
a(A002260(4))=1, so reverse the order of the next term, leaving the sequence unchanged:
            (1)
1, 2, 3, 5, (4), 6, 7, 8, 9...
a(A002260(5))=2, so reverse the order of the next 2 terms:
               (2)
1, 2, 3, 5, 4, (7, 6), 8, 9...
a(A002260(6))=3, so reverse the order of the next 3 terms:
                  (3)
1, 2, 3, 5, 4, 7, (9, 8, 6)...
		

Links

• Max Barrentine, Table of n, a(n) for n = 1..1227

Crossrefs

Cf. A000124, A002260.