A383669 Numbers whose binary representation has a positive number of 0s, all with odd runlength.

2, 5, 6, 8, 10, 11, 13, 14, 17, 21, 22, 23, 24, 26, 27, 29, 30, 32, 34, 35, 40, 42, 43, 45, 46, 47, 49, 53, 54, 55, 56, 58, 59, 61, 62, 65, 69, 70, 71, 81, 85, 86, 87, 88, 90, 91, 93, 94, 95, 96, 98, 99, 104, 106, 107, 109, 110, 111, 113, 117, 118, 119, 120

Offset: 1

Author

Clark Kimberling, May 15 2025

Keywords

• nonn
• look
• base

Examples

			The binary representation 40 is 101000, so 40 is in the sequence.
		

Links

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

Crossrefs

Cf. A060142, A383668.

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);
  if t::odd then insert([2*t],pq)
  else insert([4*t],pq)
  fi;
od:
R; # Robert Israel, Jun 16 2025

Mathematica

Map[#[[1]] &, Cases[Map[{#, # =!= {} && Apply[And, OddQ[StringLength[#]]] &[StringCases[IntegerString[#, 2], "0" ..]]} &, Range[400]], {, True}]] (* _Peter J. C. Moses, Apr 23 2025 *)

Python

def ok(n): return n&(n+1) > 0 and all(run == '' or len(run) % 2 for run in bin(n)[2:].split('1'))
print([n for n in range(121) if ok(n)]) # David Radcliffe, Jun 16 2025