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

0,3

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

Table of n, a(n) for n=0..49.

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

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 *)

Prog

(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)])

Crossrefs

Cf. A000931.

Sequence in context: A070924 A351993 A266197 * A319423 A265748 A191001

Adjacent sequences: A086635 A086636 A086637 * A086639 A086640 A086641

Keyword

easy,base,nonn

Author

David Eppstein, Sep 14 2003

Status

approved