

A038447


Sums of 5 distinct powers of 10.


6



11111, 101111, 110111, 111011, 111101, 111110, 1001111, 1010111, 1011011, 1011101, 1011110, 1100111, 1101011, 1101101, 1101110, 1110011, 1110101, 1110110, 1111001, 1111010, 1111100, 10001111, 10010111, 10011011, 10011101
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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 W. Weisstein, Mathworld: 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 !! (n1)
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

Cf. A014313 (decimal version).
Sequence in context: A346001 A032735 A308609 * A115834 A115810 A262497
Adjacent sequences: A038444 A038445 A038446 * A038448 A038449 A038450


KEYWORD

nonn,easy


AUTHOR

Olivier Gérard


STATUS

approved



