A260746 - OEIS

%I #29 Jun 01 2024 06:17:56

%S 1,4,19,83,391,1663,7739,33812,153575,677901,3075879,13586581,

%T 61458267,272367077,1228519987,5456053443,24547516939,109153816505,

%U 490067180301,2180061001275,9772927018285,43467641569472

%N Number of prime juggling patterns of period n using 4 balls.

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

%H Esther Banaian, Steve Butler, Christopher Cox, Jeffrey Davis, Jacob Landgraf and Scarlitte Ponce, <a href="http://arxiv.org/abs/1508.05296">Counting prime juggling patterns</a>, arXiv:1508.05296 [math.CO], 2015.

%H Jack Boyce, <a href="https://github.com/jkboyce/jprime">jprime program</a>, 2024.

%H Fan Chung and R. L. Graham, <a href="http://www.jstor.org/stable/27642443">Primitive juggling sequences</a>, American Mathematical Monthly 115 (2008), 185-194.

%e 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.

%Y Cf. A260744, A260745, A260752.

%K nonn,more

%O 1,2

%A _Jacob Landgraf_, Jul 30 2015

%E a(14) from _Roman Berens_, Mar 20 2021

%E a(15)-a(22) from _Jack Boyce_, May 31 2024