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

%I A086638 #20 Jul 21 2021 09:05:57
%S A086638 0,1,2,4,5,9,10,18,20,21,36,37,41,42,73,74,82,84,85,146,148,149,164,
%T A086638 165,169,170,292,293,297,298,329,330,338,340,341,585,586,594,596,597,
%U A086638 658,660,661,676,677,681,682,1170,1172,1173
%N A086638 Numbers with no 11 or 000 in their binary expansion.
%C A086638 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.
%H A086638 Chai Wah Wu, <a href="https://arxiv.org/abs/1810.02293">Record values in appending and prepending bitstrings to runs of binary digits</a>, arXiv:1810.02293 [math.NT], 2018.
%t A086638 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 *)
%t A086638 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 *)
%o A086638 (Python)
%o A086638 def A086638():
%o A086638     yield 0
%o A086638     for x in A086638():
%o A086638         if x & 3:
%o A086638             yield 2*x
%o A086638         if not (x & 1):
%o A086638             yield 2*x + 1
%o A086638 a = A086638(); print([next(a) for _ in range(100)])
%Y A086638 Cf. A000931.
%K A086638 easy,base,nonn
%O A086638 0,3
%A A086638 _David Eppstein_, Sep 14 2003