%I
%S 0,1,2,3,4,31,40,5,6,42,51,60,312,330,411,420,501,600,7,8,53,62,71,
%T 3122,3302,4013,4112,4130,4202,4400,5111,5120,5201,5300,6011,6020,
%U 7001,8000,9,423,441,450,522,531,603,612,630
%N Complete list of siteswaps (indecomposable groundstate in concatenated decimal notation organized first by sum of digits and then by magnitude).
%C Siteswaping is worthy of exploration in the elementary school classroom. In my experience (Gordon Hamilton) students across a full spectrum of ability find the subject matter intriguing and the mathematics engaging.
%C By "indecomposable" we mean that the juggling state sequence associated to each loop should not return to the ground state 7 (xxx) until after the last throw.
%C By "ground state" we mean that the permutation is chosen that is as large as possible. Example: 3302 is the same as 3023 and 0233 and 2330. Only the 3302 is in the list because it is the largest number.
%C The list breaks down at term 57, which requires a digit for "10." In the classroom this can be solved by writing "10" vertically or using commas.
%e There are 13 siteswap sequences that have a digitsum of 9. In order, these are 9, 423, 441, 450, 522, 531, 603, 612, 630, 711, 720, 801, 900.
%Y Cf. A065178, A084509, A065180.
%K hear,nonn,fini,full
%O 1,3
%A _Gordon Hamilton_, Feb 18 2015
