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

4, 9, 12, 16, 19, 25, 28, 33, 36, 39, 48, 51, 57, 60, 64, 67, 73, 76, 79, 97, 100, 103, 112, 115, 121, 124, 129, 132, 135, 144, 147, 153, 156, 159, 192, 195, 201, 204, 207, 225, 228, 231, 240, 243, 249, 252, 256, 259, 265, 268, 271, 289, 292, 295, 304, 307

Offset: 1

Author

Clark Kimberling, May 15 2025

Keywords

• nonn
• look
• base

Comments

This is a subsequence of A060142.

Examples

			The binary representation 19 is 10011, so 19 is in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A060142, A383669.

Programs

Maple

with(priqueue):
R:= NULL: count:= 0:
q:= 1:
initialize(pq);
insert([-1],pq);
while count < 100 do
  t:= op(extract(pq));
  if t = -q then q:= 2*q+1
  else R:= R,-t; count:= count+1;
  fi;
  insert([2*t-1],pq);
  insert([4*t],pq);
od:
R; # Robert Israel, Jun 16 2025

Mathematica

Map[#[[1]] &, Cases[Map[{#, # =!= {} && Apply[And, EvenQ[StringLength[#]]] &[StringCases[IntegerString[#, 2], "0" ..]]} &, Range[1000]], {, True}]] (* _Peter J. C. Moses, Apr 23 2025 *)