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

Author

Jeffrey Davis, Jul 30 2015

Keywords

• nonn
• more

Comments

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

Examples

			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.
		

Links

• 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.

Crossrefs

Cf. A260744, A260745, A260746.

Extensions

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

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