cp's OEIS Frontend

A383668 Numbers whose binary representation has a positive number of 0s, all with even runlength.

%I A383668 #16 Jun 18 2025 01:00:49
%S A383668 4,9,12,16,19,25,28,33,36,39,48,51,57,60,64,67,73,76,79,97,100,103,
%T A383668 112,115,121,124,129,132,135,144,147,153,156,159,192,195,201,204,207,
%U A383668 225,228,231,240,243,249,252,256,259,265,268,271,289,292,295,304,307
%N A383668 Numbers whose binary representation has a positive number of 0s, all with even runlength.
%C A383668 This is a subsequence of A060142.
%H A383668 Robert Israel, <a href="/A383668/b383668.txt">Table of n, a(n) for n = 1..10000</a>
%e A383668 The binary representation 19 is 10011, so 19 is in the sequence.
%p A383668 with(priqueue):
%p A383668 R:= NULL: count:= 0:
%p A383668 q:= 1:
%p A383668 initialize(pq);
%p A383668 insert([-1],pq);
%p A383668 while count < 100 do
%p A383668   t:= op(extract(pq));
%p A383668   if t = -q then q:= 2*q+1
%p A383668   else R:= R,-t; count:= count+1;
%p A383668   fi;
%p A383668   insert([2*t-1],pq);
%p A383668   insert([4*t],pq);
%p A383668 od:
%p A383668 R; # _Robert Israel_, Jun 16 2025
%t A383668 Map[#[[1]] &, Cases[Map[{#, # =!= {} && Apply[And, EvenQ[StringLength[#]]] &[StringCases[IntegerString[#, 2], "0" ..]]} &, Range[1000]], {_, True}]] (* _Peter J. C. Moses_, Apr 23 2025 *)
%Y A383668 Cf. A060142, A383669.
%K A383668 nonn,look,base
%O A383668 1,1
%A A383668 _Clark Kimberling_, May 15 2025