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A268412
Balanced evil numbers: numbers with an even number of runs of 1's in their binary expansion.
6
0, 5, 9, 10, 11, 13, 17, 18, 19, 20, 22, 23, 25, 26, 27, 29, 33, 34, 35, 36, 38, 39, 40, 44, 46, 47, 49, 50, 51, 52, 54, 55, 57, 58, 59, 61, 65, 66, 67, 68, 70, 71, 72, 76, 78, 79, 80, 85, 88, 92, 94, 95, 97, 98, 99, 100, 102, 103, 104, 108, 110, 111, 113, 114
OFFSET
0,2
COMMENTS
In balanced binary system the sequence A268411 plays role of Thue-Morse sequence (A010060). Therefore, we call the balanced evil numbers those numbers n for which A268411(n) = 0.
LINKS
Peter J. C. Moses (terms 0..999) & Antti Karttunen, Table of n, a(n) for n = 0..8256
Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.
FORMULA
Other identities. For all n >= 0:
A268383(a(n)) = n.
EXAMPLE
In binary representation 19=10011 has an even number (two) of runs of 1's. So, 19 is a member.
MATHEMATICA
balancedBinary:=Join[#, {0}]-Join[{0}, #]&[IntegerDigits[#, 2]]&;
Flatten[Position[Map[Mod[Count[balancedBinary[#], 1], 2]&, Range[0, 100]], 0, 1]-1] (* Peter J. C. Moses, Feb 04 2016 *)
PROG
(Python)
A268412_list = [i for i in range(10**6) if not len(list(filter(bool, format(i, 'b').split('0')))) % 2] # Chai Wah Wu, Mar 01 2016
CROSSREFS
Positions of even terms in A069010.
Cf. A268415 (complement).
Cf. A268383 (the least monotonic left inverse).
Cf. A268476 (primes in this sequence).
Sequence in context: A166934 A257739 A094695 * A043682 A335882 A111102
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Feb 04 2016
EXTENSIONS
More terms from Peter J. C. Moses, Feb 04 2016
STATUS
approved