%I #17 Feb 21 2023 07:33:08
%S 11111,101111,110111,111011,111101,111110,1001111,1010111,1011011,
%T 1011101,1011110,1100111,1101011,1101101,1101110,1110011,1110101,
%U 1110110,1111001,1111010,1111100,10001111,10010111,10011011,10011101
%N Sums of 5 distinct powers of 10.
%C From _Joshua S.M. Weiner_, Oct 18 2012: (Start)
%C It is also the "energy state" of 5 quantum (objects) in "siteswap" juggling patterns.
%C This is also the binary representation of nC5 for n = 5 to infinity.
%C A siteswap example: 85525.
%C a(n) = [decimal] = [binary] = transition notes.
%C a(1) = [31] = 11111 = the ground state "5" throw.
%C a(22) = [143] = 1001111 = can be reached from a(1) with an "8" throw.
%C a(12) = [103] = 110111 = can be reached from a(22) with a "5" throw.
%C a(4) = [55] = 111011 = can be reached from a(12) with a "5" throw.
%C a(1) = [31] = 11111 = can be reached from a(4) with a "2".
%C a(1) = [31] = 11111 = can be repeated from a(1) with a "5" throw.
%C (End)
%H Reinhard Zumkeller, <a href="/A038447/b038447.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Siteswap.html">Siteswap</a>
%e From _Joshua S.M. Weiner_, Oct 18 2012: (Start)
%e a(1) = 11111
%e a(2) = 101111 (begins 6C5 nodes)
%e a(3) = 110111
%e a(4) = 111011
%e a(5) = 111101
%e a(6) = 111110
%e a(7) = 1001111 (begins 7C5 nodes)
%e (End)
%t t = Select[Range[200], Total[IntegerDigits[#, 2]] == 5 &]; FromDigits /@ IntegerDigits[t, 2] (* _T. D. Noe_, Oct 19 2012 *)
%o (Haskell)
%o import Data.Set (fromList, deleteFindMin, union)
%o a038447 n = a038447_list !! (n-1)
%o a038447_list = f $ fromList [11111] where
%o f s = m : f (union s' $ fromList $ g [] $ show m) where
%o (m, s') = deleteFindMin s
%o g _ [] = []
%o g us ('0':vs) = g (us ++ ['0']) vs
%o g us ('1':vs) = (read (us ++ "10" ++ vs)) : g (us ++ ['1']) vs
%o -- _Reinhard Zumkeller_, Jan 06 2015
%Y Cf. A011557, A014313 (decimal version).
%K nonn,easy
%O 1,1
%A _Olivier Gérard_