
COMMENTS

Each subgroup {0,a,b,...} of nimber addition can be assigned an integer 1+2^a+2^b+...
These integers ordered by size give this sequence.
Without nimbers the sequence may be defined as follows:
The powerset af a set {0,...,n1} with the symmetric difference as group operation forms the elementary abelian group (Z_2)^n.
The elements of the group can be numbered lexicographically from 0 to 2^n1, with 0 representing the neutral element:
{}>0 , {0}>2^0=1 , {1}>2^1=2 , {0,1}>2^0+2^1=3 , ... , {0,...,n1}>2^n1
So the subroups of (Z_2)^n can be represented by subsets of {0,...,2^n1}.
So each subgroup {0,a,b,...} of (Z_2)^n can be assigned an integer 1+2^a+2^b+...
For each (Z_2)^n there is a finite sequence of these numbers ordered by size, and it is the beginning of the finite sequence for (Z_2)^(n+1).
This leads to the infinite sequence:
* 1, (1 until here for (Z_2)^0)
* 3, (2 until here for (Z_2)^1)
* 5, 9, 15, (5 until here for (Z_2)^2)
* 17, 33, 51, 65, 85, 105, 129, 153, 165, 195, 255, (16 until here for (Z_2)^3)
* 257, 513, 771, 1025, 1285, 1545, 2049, 2313, 2565, 3075, 3855, 4097, 4369, 4641, 5185, 6273, 8193, 8481, 8721, 9345, 10305, 12291, 13107, 15555, 16385, 16705, 17025, 17425, 18465, 20485, 21845, 23205, 24585, 26265, 26985, 32769, 33153, 33345, 33825, 34833, 36873, 38505, 39321, 40965, 42405, 43605, 49155, 50115, 52275, 61455, 65535, (67 until here for (Z_2)^4)
* 65537, ...
The number of subgroups of (Z_2)^n is 1, 2, 5, 16, 67, 374, 2825, ... (A006116)
Comment from Tilman Piesk, Aug 27 2013: (Start)
Boolean functions correspond to integers, and belong to small equivalence classes (sec). So a sec can be seen as an infinite set of integers (represented in A227722 by the smallest one). Some secs contain only one odd integer. These unique odd integers, ordered by size, are shown in this sequence. (While the smallest integers from these secs are shown in A227963.)
(End)
