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

Author

Olivier Gérard

Keywords

• nonn
• easy

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)

Examples

			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)
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Siteswap

Crossrefs

Cf. A011557, A014313 (decimal version).

Programs

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

Mathematica

t = Select[Range[200], Total[IntegerDigits[#, 2]] == 5 &]; FromDigits /@ IntegerDigits[t, 2] (* T. D. Noe, Oct 19 2012 *)

Python

from itertools import islice
def A038447_gen(): # generator of terms
    yield int(bin(n:=31)[2:])
    while True: yield int(bin((n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b))[2:])
A038447_list = list(islice(A038447_gen(),20)) # Chai Wah Wu, Mar 11 2025