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 A090079 In binary expansion of n: reduce contiguous blocks of 0's to 0 and contiguous blocks of 1's to 1. 10
 0, 1, 2, 1, 2, 5, 2, 1, 2, 5, 10, 5, 2, 5, 2, 1, 2, 5, 10, 5, 10, 21, 10, 5, 2, 5, 10, 5, 2, 5, 2, 1, 2, 5, 10, 5, 10, 21, 10, 5, 10, 21, 42, 21, 10, 21, 10, 5, 2, 5, 10, 5, 10, 21, 10, 5, 2, 5, 10, 5, 2, 5, 2, 1, 2, 5, 10, 5, 10, 21, 10, 5, 10, 21, 42, 21, 10, 21, 10, 5, 10, 21, 42, 21 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(a(n))=a(n); a(n)=A090078(A090077(n))=A090077(A090078(n)). All terms are without consecutive equal binary digits: a(A000975(n)) = A000975(n) and a(m) <> A000975(n) for m < A000975(n). - Reinhard Zumkeller, Feb 16 2013 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 Index entries for sequences related to binary expansion of n FORMULA Conjecture: a(n) = (2^(A005811(n)+1) + (1-(-1)^n)/2 - 2)/3. - Velin Yanev, Dec 12 2016 EXAMPLE 100 -> '1100100' -> [11][00][1][00] -> [1][0][1][0] -> '1010' -> 10=a(100). MATHEMATICA Table[FromDigits[#, 2] &@ Map[First, Split@ IntegerDigits[n, 2]], {n, 0, 83}] (* Michael De Vlieger, Dec 12 2016 *) FromDigits[Split[IntegerDigits[#, 2]][[All, 1]], 2]&/@Range[0, 90] (* Harvey P. Dale, Oct 10 2017 *) PROG (Haskell) a090079 = foldr (\b v -> 2 * v + b) 0 . map head . group . a030308_row -- Reinhard Zumkeller, Feb 16 2013 (Python) from itertools import groupby def a(n): return int("".join(k for k, g in groupby(bin(n)[2:])), 2) print([a(n) for n in range(84)]) # Michael S. Branicky, Jul 23 2022 CROSSREFS Cf. A007088, A090077, A090078, A090080. Cf. A030308, A005811. Sequence in context: A068822 A351517 A337224 * A165195 A121487 A057031 Adjacent sequences: A090076 A090077 A090078 * A090080 A090081 A090082 KEYWORD nonn,base AUTHOR Reinhard Zumkeller, Nov 20 2003 STATUS approved

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Last modified August 8 12:42 EDT 2024. Contains 375021 sequences. (Running on oeis4.)