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Natural numbers which map to the cyclic partitions; cf. A140691 for the complete set.
1

%I #3 Mar 31 2012 13:23:39

%S 1,2,4,8,6,16,10,32,18,12,14,64,34,20,22,128,66,36,38,24,26,30,256,

%T 130,68,70,40,42,46,28,512,258,132,134,72,74,78,44

%N Natural numbers which map to the cyclic partitions; cf. A140691 for the complete set.

%C Note that A002865 gives the number of entries per column.

%e Table A140691 begins

%e 1..2..4..8..16..32

%e ..3..5..9..17..33

%e .....7.11..19..35

%e .......15..23..39

%e ...........31..47

%e ...............63

%e .................

%e ........6..10..18

%e ...........13..21

%e ...............27

%e since each matching case, say x, is generated by the rule "2x+1",

%e only the even cases map to cyclic partitions; so the sequence begins

%e 1..2..4..8..16..32

%e ........6..10..18

%e ...............12

%e ...............14

%Y Cf. A002865, A140691.

%K nonn

%O 1,2

%A _Alford Arnold_, May 23 2008