

A271863


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


2



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
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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



