A383669 Numbers whose binary representation has a positive number of 0's, 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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A060142, A383668.

Sequence in context: A176590 A253061 A320730 * A087943 A034020 A395965

Adjacent sequences: A383666 A383667 A383668 * A383670 A383671 A383672

Keyword

nonn,look,base

Author

Clark Kimberling, May 15 2025

Status

approved