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A271865
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Recursive sequence based on the central polygonal numbers (A000124) and A004738.
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2
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1, 2, 4, 3, 6, 9, 7, 8, 10, 13, 5, 15, 12, 14, 16, 19, 11, 23, 20, 17, 22, 18, 24, 27, 21, 31, 35, 28, 32, 34, 26, 33, 29, 37, 25, 41, 45, 39, 47, 30, 44, 46, 42, 40, 36, 49, 43, 53, 57, 51, 58, 50, 61, 54, 52, 60, 55, 59, 38, 63, 56, 67, 71, 65, 72, 75, 70
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OFFSET
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1,2
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COMMENTS
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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(A004738(n)) numbers.
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LINKS
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EXAMPLE
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Start with the natural numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9...
a(A004738(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(A004738(2))=2, so reverse the order of the next 2 terms:
(2)
1, 2, (4, 3), 5, 6, 7, 8, 9...
a(A004738(3))=1, so reverse the order of the next term, leaving the sequence unchanged:
(1)
1, 2, 4, (3), 5, 6, 7, 8, 9...
a(A004738(4))=2, so reverse the order of the next 2 terms:
(2)
1, 2, 4, 3, (6, 5), 7, 8, 9...
a(A004738(5))=4, so reverse the order of the next 4 terms:
(4)
1, 2, 4, 3, 6, (9, 8, 7, 5)...
a(A004738(6))=2, so reverse the order of the next 2 terms:
(2)
1, 2, 4, 3, 6, 9, (7, 8), 5...
a(A004738(7))=1, so reverse the order of the next term, leaving the sequence unchanged:
(1)
1, 2, 4, 3, 6, 9, 7, (8), 5...
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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