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

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, 26, 31, 27, 39, 20, 38, 40, 33, 35, 30, 34, 49, 36, 46, 37, 21, 45, 43, 48, 44, 51, 59, 41, 56, 42, 50, 55, 53, 58, 54, 67, 62, 70, 64, 57, 65, 63, 52, 60, 69, 47

Offset

1,2

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(A004736(n)) numbers.

Links

Max Barrentine, Table of n, a(n) for n = 1..1082

Example

Start with the natural numbers:
1, 2, 3, 4, 5, 6, 7, 8...
a(A004736(1))=1, so reverse the order of the next term, leaving the sequence unchanged:
   (1)
1, (2), 3, 4, 5, 6, 7, 8...
a(A004736(2))=2, so reverse the order of the next 2 terms:
      (2)
1, 2, (4, 3), 5, 6, 7, 8, 9...
a(A004736(3))=1, so reverse the order of the next term, leaving the sequence unchanged:
         (1)
1, 2, 4, (3), 5, 6, 7, 8...
a(A004736(4))=4, so reverse the order of the next 4 terms:
            (4)
1, 2, 4, 3, (8, 7, 6, 5)...
a(A004736(5))=2, so reverse the order of the next 2 terms:
               (2)
1, 2, 4, 3, 8, (6, 7), 5...
a(A004736(6))=1, so reverse the order of the next term, leaving the sequence unchanged:
                  (1)
1, 2, 4, 3, 8, 6, (7), 5...

Crossrefs

Cf. A000124, A004736.

Sequence in context: A127301 A209636 A243491 * A341220 A253563 A294044

Adjacent sequences: A271860 A271861 A271862 * A271864 A271865 A271866

Keyword

nonn

Author

Max Barrentine, Apr 15 2016

Status

approved