A260746 Number of prime juggling patterns of period n using 4 balls.

1, 4, 19, 83, 391, 1663, 7739, 33812, 153575, 677901, 3075879, 13586581, 61458267, 272367077, 1228519987, 5456053443, 24547516939, 109153816505, 490067180301, 2180061001275, 9772927018285, 43467641569472

Offset

1,2

Comments

A juggling pattern is prime if the closed walk corresponding to the pattern in the juggling state graph is a cycle.

Links

Table of n, a(n) for n=1..22.

Esther Banaian, Steve Butler, Christopher Cox, Jeffrey Davis, Jacob Landgraf and Scarlitte Ponce, Counting prime juggling patterns, arXiv:1508.05296 [math.CO], 2015.

Jack Boyce, jprime program, 2024.

Fan Chung and R. L. Graham, Primitive juggling sequences, American Mathematical Monthly 115 (2008), 185-194.

Example

In siteswap notation, the prime juggling pattern(s) of length one is 4; of length two are 53, 62, 71 and 80; of length three are (11)01, (12)00, 660, 750, (10)11, (10)20, 390, 831, 822, 471, 561, 741, 723, 633, 642, 552, 912, 930 and 480.

Crossrefs

Cf. A260744, A260745, A260752.

Sequence in context: A017961 A180146 A017962 * A290667 A357572 A291416

Adjacent sequences: A260743 A260744 A260745 * A260747 A260748 A260749

Keyword

nonn,more

Author

Jacob Landgraf, Jul 30 2015

Extensions

a(14) from Roman Berens, Mar 20 2021

a(15)-a(22) from Jack Boyce, May 31 2024

Status

approved