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 A053754 If k is in the sequence then 2*k and 2*k+1 are not (and 0 is in the sequence); when written in binary k has an even number of bits (0 has 0 digits). 47
 0, 2, 3, 8, 9, 10, 11, 12, 13, 14, 15, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Runs of successive terms with same number of bits have length twice powers of 4 (A081294). [Clarified by Michel Marcus, Oct 21 2020] The sequence A081294 counts compositions of even numbers - Gus Wiseman, Aug 12 2021 A031443 is a subsequence; A179888 is the intersection of this sequence and A032925. - Reinhard Zumkeller, Jul 31 2010 The lower and upper asymptotic densities of this sequence are 1/3 and 2/3, respectively. - Amiram Eldar, Feb 01 2021 From Gus Wiseman, Aug 10 2021: (Start) Also numbers k such that the k-th composition in standard order (row k of A066099) has even sum. The terms and corresponding compositions begin: 0: () 2: (2) 8: (4) 3: (1,1) 9: (3,1) 10: (2,2) 11: (2,1,1) 12: (1,3) 13: (1,2,1) 14: (1,1,2) 15: (1,1,1,1) The following pertain to compositions in standard order: A000120, A029837, A070939, A066099, A124767. (End) LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10001 MATHEMATICA Select[Range[0, 150], EvenQ @ IntegerLength[#, 2] &] (* Amiram Eldar, Feb 01 2021 *) PROG (Haskell) a053754 n = a053754_list !! (n-1) a053754_list = 0 : filter (even . a070939) [1..] -- Reinhard Zumkeller, Apr 18 2015 (PARI) lista(nn) = {my(va = vector(nn)); for (n=2, nn, my(k=va[n-1]+1); while (#select(x->(x==k\2), va), k++); va[n] = k; ); va; } \\ Michel Marcus, Oct 20 2020 (PARI) a(n) = n-1 + (1<

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Last modified September 17 05:28 EDT 2024. Contains 375985 sequences. (Running on oeis4.)