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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 (list; graph; refs; listen; history; text; internal format)
 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. A010060, A001969, A268411. Cf. A268415 (complement). Cf. A268383 (the least monotonic left inverse). Cf. A268476 (primes in this sequence). Sequence in context: A166934 A257739 A094695 * A043682 A111102 A139456 Adjacent sequences:  A268409 A268410 A268411 * A268413 A268414 A268415 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 21 20:30 EDT 2019. Contains 321382 sequences. (Running on oeis4.)