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A086638
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Numbers with no 11 or 000 in their binary expansion.
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3
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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(Python)
yield 0
if x & 3:
yield 2*x
if not (x & 1):
yield 2*x + 1
a = A086638(); print([next(a) for _ in range(100)])
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CROSSREFS
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KEYWORD
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easy,base,nonn
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AUTHOR
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STATUS
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approved
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