A086638 Numbers with no 11 or 000 in their binary expansion.

0, 1, 2, 4, 5, 9, 10, 18, 20, 21, 36, 37, 41, 42, 73, 74, 82, 84, 85, 146, 148, 149, 164, 165, 169, 170, 292, 293, 297, 298, 329, 330, 338, 340, 341, 585, 586, 594, 596, 597, 658, 660, 661, 676, 677, 681, 682, 1170, 1172, 1173

Offset: 0

Author

David Eppstein, Sep 14 2003

Keywords

• easy
• base
• nonn

Comments

The number of n-bit numbers in this sequence for n>1 is given by a(n+6) where a is the Padovan sequence A000931.

Links

• Chai Wah Wu, Record values in appending and prepending bitstrings to runs of binary digits, arXiv:1810.02293 [math.NT], 2018.

Crossrefs

Cf. A000931.

Programs

Mathematica

Select[Range[0, 1200], And[AllTrue[#1, # < 2 &], AllTrue[#2, # < 3 &]] & @@ {Part[#, 2 Range@ Ceiling[Length[#]/2] - 1], Part[#, 2 Range@ Floor[Length[#]/2]]} &@ Map[Length, Split@ IntegerDigits[#, 2]] &] (* Michael De Vlieger, Dec 26 2018 *)
Select[Range[0,1200],SequenceCount[IntegerDigits[#,2],{1,1}] == SequenceCount[ IntegerDigits[ #,2],{0,0,0}]==0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 16 2019 *)

Python

def A086638():
    yield 0
    for x in A086638():
        if x & 3:
            yield 2*x
        if not (x & 1):
            yield 2*x + 1
a = A086638(); print([next(a) for _ in range(100)])