A255253 Complete list of siteswaps (indecomposable ground-state in concatenated decimal notation organized first by sum of digits and then by magnitude).

0, 1, 2, 3, 4, 31, 40, 5, 6, 42, 51, 60, 312, 330, 411, 420, 501, 600, 7, 8, 53, 62, 71, 3122, 3302, 4013, 4112, 4130, 4202, 4400, 5111, 5120, 5201, 5300, 6011, 6020, 7001, 8000, 9, 423, 441, 450, 522, 531, 603, 612, 630

Offset: 1

Author

Gordon Hamilton, Feb 18 2015

Keywords

• hear
• nonn
• fini
• full

Comments

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.

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.

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.

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.

Examples

			There are 13 siteswap sequences that have a digit-sum of 9. In order, these are 9, 423, 441, 450, 522, 531, 603, 612, 630, 711, 720, 801, 900.
		

Crossrefs

Cf. A065178, A084509, A065180.