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A268415 Balanced odious numbers: numbers with an odd number of runs of 1's in their binary expansion. 7
1, 2, 3, 4, 6, 7, 8, 12, 14, 15, 16, 21, 24, 28, 30, 31, 32, 37, 41, 42, 43, 45, 48, 53, 56, 60, 62, 63, 64, 69, 73, 74, 75, 77, 81, 82, 83, 84, 86, 87, 89, 90, 91, 93, 96, 101, 105, 106, 107, 109, 112, 117, 120, 124, 126, 127, 128, 133, 137, 138, 139, 141 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
In the balanced binary system the sequence A268411 plays the role of the Thue-Morse sequence (A010060). Therefore we call the balanced odious numbers those numbers n for which A268411(n) = 1.
Complement of A268412.
LINKS
Peter J. C. Moses (terms 1..1000) & Antti Karttunen, Table of n, a(n) for n = 1..8129
Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.
FORMULA
Other identities. For all n >= 1:
A268382(a(n)) = n.
EXAMPLE
Since in the binary 77=1001101 has odd number three) runs of 1's, then 77 is a member.
MATHEMATICA
balancedBinary:=Join[#, {0}]-Join[{0}, #]&[IntegerDigits[#, 2]]&;
Flatten[Position[Map[Mod[Count[balancedBinary[#], 1], 2]&, Range[0, 100]], 1]-1] (* Peter J. C. Moses, Feb 04 2016 *)
Select[Range[200], OddQ[Count[Split[IntegerDigits[#, 2]], _?(MemberQ[ #, 1]&)]]&] (* Harvey P. Dale, Mar 31 2019 *)
PROG
(Scheme) (define A268415 (ZERO-POS 1 1 (COMPOSE -1+ A268411))) ;; requires also my IntSeq-library. - Antti Karttunen, Feb 05 2016
(Python)
A268415_list = [i for i in range(10**6) if len(list(filter(bool, format(i, 'b').split('0')))) % 2] # Chai Wah Wu, Mar 01 2016
CROSSREFS
Positions of odd terms in A069010.
Cf. A268412 (complement).
Cf. A268382 (the least monotonic left inverse).
Cf. A268477 (primes in this sequence).
Sequence in context: A191281 A032900 A370684 * A352084 A277779 A166935
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Feb 04 2016
EXTENSIONS
More terms from Peter J. C. Moses, Feb 04 2016
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)