A038447 Sums of 5 distinct powers of 10.

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

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

Cf. A011557, 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