A221714 Numbers written in base 2 with digits rearranged to be in decreasing order.

0, 1, 10, 11, 100, 110, 110, 111, 1000, 1100, 1100, 1110, 1100, 1110, 1110, 1111, 10000, 11000, 11000, 11100, 11000, 11100, 11100, 11110, 11000, 11100, 11100, 11110, 11100, 11110, 11110, 11111, 100000, 110000, 110000, 111000, 110000

Offset: 0

Author

Bruce L. Rothschild and N. J. A. Sloane, Jan 26 2013

Keywords

• nonn
• base
• easy

Comments

This is the base-2 equivalent of A004186.

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..10000

Crossrefs

For decimal equivalents see A073138.

Cf. A004086, A004185, A004186, A009996.

Programs

Maple

a:= n-> parse(cat(0, sort(Bits[Split](n), `>`)[])):
seq(a(n), n=0..36);  # Alois P. Heinz, Aug 18 2025

Mathematica

a[n_] := FromDigits[-Sort[-IntegerDigits[n, 2]]] (* Giovanni Resta, Jan 27 2013 *)

Python

def a(n):
     return "".join(sorted(bin(n)[2:],reverse=True)) # Indranil Ghosh, Jan 09 2017

Python

def A221714(n): return int(bin((m:=1<>n.bit_count()))[2:]) # Chai Wah Wu, Aug 18 2025

Extensions

a(18)-a(36) from Giovanni Resta, Jan 27 2013