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

%I A221714 #17 Aug 18 2025 20:39:26
%S A221714 0,1,10,11,100,110,110,111,1000,1100,1100,1110,1100,1110,1110,1111,
%T A221714 10000,11000,11000,11100,11000,11100,11100,11110,11000,11100,11100,
%U A221714 11110,11100,11110,11110,11111,100000,110000,110000,111000,110000
%N A221714 Numbers written in base 2 with digits rearranged to be in decreasing order.
%C A221714 This is the base-2 equivalent of A004186.
%H A221714 Indranil Ghosh, <a href="/A221714/b221714.txt">Table of n, a(n) for n = 0..10000</a>
%p A221714 a:= n-> parse(cat(0, sort(Bits[Split](n), `>`)[])):
%p A221714 seq(a(n), n=0..36);  # _Alois P. Heinz_, Aug 18 2025
%t A221714 a[n_] := FromDigits[-Sort[-IntegerDigits[n, 2]]] (* _Giovanni Resta_, Jan 27 2013 *)
%o A221714 (Python)
%o A221714 def a(n):
%o A221714      return "".join(sorted(bin(n)[2:],reverse=True)) # _Indranil Ghosh_, Jan 09 2017
%o A221714 (Python)
%o A221714 def A221714(n): return int(bin((m:=1<<n.bit_length())-(m>>n.bit_count()))[2:]) # _Chai Wah Wu_, Aug 18 2025
%Y A221714 For decimal equivalents see A073138.
%Y A221714 Cf. A004086, A004185, A004186, A009996.
%K A221714 nonn,base,easy
%O A221714 0,3
%A A221714 Bruce L. Rothschild and _N. J. A. Sloane_, Jan 26 2013
%E A221714 a(18)-a(36) from _Giovanni Resta_, Jan 27 2013