login
A271861
Recursive sequence based on the central polygonal numbers (A000124) and A002260.
2
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
1,2
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(A002260(n)) numbers.
LINKS
EXAMPLE
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)...
CROSSREFS
Sequence in context: A102399 A118318 A245707 * A084937 A344307 A347179
KEYWORD
nonn
AUTHOR
Max Barrentine, Apr 15 2016
STATUS
approved