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

Author

Tilman Piesk, Aug 08 2013

Keywords

• nonn

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.

Examples

			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.
		

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