OFFSET
1,1
COMMENTS
From Joshua S.M. Weiner, Oct 18 2012: (Start)
It is also the "energy state" of 5 quantum (objects) in "siteswap" juggling patterns.
This is also the binary representation of nC5 for n = 5 to infinity.
A siteswap example: 85525.
a(n) = [decimal] = [binary] = transition notes.
a(1) = [31] = 11111 = the ground state "5" throw.
a(22) = [143] = 1001111 = can be reached from a(1) with an "8" throw.
a(12) = [103] = 110111 = can be reached from a(22) with a "5" throw.
a(4) = [55] = 111011 = can be reached from a(12) with a "5" throw.
a(1) = [31] = 11111 = can be reached from a(4) with a "2".
a(1) = [31] = 11111 = can be repeated from a(1) with a "5" throw.
(End)
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Siteswap
EXAMPLE
From Joshua S.M. Weiner, Oct 18 2012: (Start)
a(1) = 11111
a(2) = 101111 (begins 6C5 nodes)
a(3) = 110111
a(4) = 111011
a(5) = 111101
a(6) = 111110
a(7) = 1001111 (begins 7C5 nodes)
(End)
MATHEMATICA
t = Select[Range[200], Total[IntegerDigits[#, 2]] == 5 &]; FromDigits /@ IntegerDigits[t, 2] (* T. D. Noe, Oct 19 2012 *)
PROG
(Haskell)
import Data.Set (fromList, deleteFindMin, union)
a038447 n = a038447_list !! (n-1)
a038447_list = f $ fromList [11111] where
f s = m : f (union s' $ fromList $ g [] $ show m) where
(m, s') = deleteFindMin s
g _ [] = []
g us ('0':vs) = g (us ++ ['0']) vs
g us ('1':vs) = (read (us ++ "10" ++ vs)) : g (us ++ ['1']) vs
-- Reinhard Zumkeller, Jan 06 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved