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A255253 Complete list of siteswaps (indecomposable ground-state in concatenated decimal notation organized first by sum of digits and then by magnitude). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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.

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

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.

Sequence in context: A064889 A057917 A250189 * A076592 A004844 A037324

Adjacent sequences:  A255250 A255251 A255252 * A255254 A255255 A255256

KEYWORD

hear,nonn,fini,full

AUTHOR

Gordon Hamilton, Feb 18 2015

STATUS

approved

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Last modified August 21 05:40 EDT 2019. Contains 326162 sequences. (Running on oeis4.)