A227963 Small equivalence classes (A227722) of subgroups of nimber addition (A190939).

1, 3, 5, 6, 15, 17, 18, 51, 20, 85, 105, 24, 102, 90, 60, 255, 257, 258, 771, 260, 1285, 1545, 264, 1542, 1290, 780, 3855, 272, 4369, 4641, 5185, 6273, 288, 4626, 4386, 6210, 5250, 816, 13107, 15555, 320, 5140, 6180, 4420, 4740, 1360, 21845

Offset

0,2

Comments

Each entry of this sequence represents the same small equivalence class (sec) of Boolean functions as the corresponding entry of A190939. While A190939 represents each sec by the unique odd number among the numeric values of its functions, this sequence represents each sec by the smallest among these numbers (as an entry of A227722).

All big equivalence classes (bec) of Boolean functions are also small equivalence classes. So all entries in the sequence of sona-becs (A227960) are also in this sequence of sona-secs.

This sequence takes its order from A190939, so it is not monotonic. Thus it is not a subsequence of A227722, and does not contain A227960 as a subsequence.

First entries: 1, 3, 5, 6, 15, 17, 18, 51, 20, 85, 105, 24, 102, 90, 60, 255.

First entries in numerical order: 1, 3, 5, 6, 15, 17, 18, 20, 24, 51, 60, 85, 90, 102, 105, 255.

Links

Tilman Piesk, Table of n, a(n) for n = 0..2824

Tilman Piesk, Table of n, A190939(n), a(n) for n = 0..2824 and the same with a graphical explanation for n = 0..66

Tilman Piesk, Subgroups of nimber addition (Wikiversity)

Tilman Piesk, Small equivalence classes of Boolean functions

Example

A190939(3) = 9. 9 belongs to the sec A227722(4) = 6. So a(3) = 6.
A190939(8) = 65. 65 belongs to the sec A227722(10) = 20. So a(8) = 20.

Crossrefs

Sequence in context: A298563 A180694 A030052 * A099678 A287687 A348658

Adjacent sequences: A227960 A227961 A227962 * A227964 A227965 A227966

Keyword

nonn

Author

Tilman Piesk, Aug 08 2013

Status

approved