A260752 Number of prime juggling patterns of period n using 5 balls.

1, 5, 29, 157, 901, 4822, 27447, 149393, 836527, 4610088, 25846123, 142296551, 799268609, 4426204933, 24808065829, 137945151360, 773962487261, 4310815784117, 24208263855765

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..19.

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 5; of length two are 64, 73, 82, 91 and (10)0; of length three are (11)31, (11)22, 4(10)1, 3(12)0, (13)20, (13)11, 591, (10)23, (10)41, 960, 780, 663, 744, 753, 4(11)0, (12)12, (12)30, 771, 861, (15)00, 933, 942, 582, (10)50, 690, (14)01, 852, 834 and 672.

Crossrefs

Cf. A260744, A260745, A260746.

Sequence in context: A320089 A377294 A239715 * A098780 A222700 A272940

Adjacent sequences: A260749 A260750 A260751 * A260753 A260754 A260755

Keyword

nonn,more

Author

Jeffrey Davis, Jul 30 2015

Extensions

a(12)-a(13) from Roman Berens, Mar 20 2021

a(14)-a(19) from Jack Boyce, May 31 2024

Status

approved