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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 (list; graph; refs; listen; history; text; internal format)
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 !! (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. 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

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)