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Sums of 5 distinct powers of 10.
15

%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 GĂ©rard_