cp's OEIS Frontend

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

%I A227963 #18 Aug 09 2013 14:17:09
%S A227963 1,3,5,6,15,17,18,51,20,85,105,24,102,90,60,255,257,258,771,260,1285,
%T A227963 1545,264,1542,1290,780,3855,272,4369,4641,5185,6273,288,4626,4386,
%U A227963 6210,5250,816,13107,15555,320,5140,6180,4420,4740,1360,21845
%N A227963 Small equivalence classes (A227722) of subgroups of nimber addition (A190939).
%C A227963 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).
%C A227963 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.
%C A227963 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.
%C A227963 First entries: 1, 3, 5, 6, 15, 17, 18, 51, 20, 85, 105, 24, 102, 90, 60, 255.
%C A227963 First entries in numerical order: 1, 3, 5, 6, 15, 17, 18, 20, 24, 51, 60, 85, 90, 102, 105, 255.
%H A227963 Tilman Piesk, <a href="/A227963/b227963.txt">Table of n, a(n) for n = 0..2824</a>
%H A227963 Tilman Piesk, <a href="/A227963/a227963_1.txt">Table of n, A190939(n), a(n) for n = 0..2824</a> and <a href="http://commons.wikimedia.org/wiki/File:Z2%5E4;_subgroups_list.svg#File">the same with a graphical explanation for n = 0..66</a>
%H A227963 Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Subgroups_of_nimber_addition">Subgroups of nimber addition</a> (Wikiversity)
%H A227963 Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Equivalence_classes_of_Boolean_functions#sec">Small equivalence classes of Boolean functions</a>
%e A227963 A190939(3) = 9. 9 belongs to the sec A227722(4) = 6. So a(3) = 6.
%e A227963 A190939(8) = 65. 65 belongs to the sec A227722(10) = 20. So a(8) = 20.
%K A227963 nonn
%O A227963 0,2
%A A227963 _Tilman Piesk_, Aug 08 2013