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
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
Programs
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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
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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