# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a053754 Showing 1-1 of 1 %I A053754 #45 Sep 20 2021 22:19:20 %S A053754 0,2,3,8,9,10,11,12,13,14,15,32,33,34,35,36,37,38,39,40,41,42,43,44, %T A053754 45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,128,129,130, %U A053754 131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148 %N 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). %C A053754 Runs of successive terms with same number of bits have length twice powers of 4 (A081294). [Clarified by _Michel Marcus_, Oct 21 2020] %C A053754 The sequence A081294 counts compositions of even numbers - _Gus Wiseman_, Aug 12 2021 %C A053754 A031443 is a subsequence; A179888 is the intersection of this sequence and A032925. - _Reinhard Zumkeller_, Jul 31 2010 %C A053754 The lower and upper asymptotic densities of this sequence are 1/3 and 2/3, respectively. - _Amiram Eldar_, Feb 01 2021 %C A053754 From _Gus Wiseman_, Aug 10 2021: (Start) %C A053754 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: %C A053754 0: () 2: (2) 8: (4) %C A053754 3: (1,1) 9: (3,1) %C A053754 10: (2,2) %C A053754 11: (2,1,1) %C A053754 12: (1,3) %C A053754 13: (1,2,1) %C A053754 14: (1,1,2) %C A053754 15: (1,1,1,1) %C A053754 The following pertain to compositions in standard order: A000120, A029837, A070939, A066099, A124767. %C A053754 (End) %H A053754 Reinhard Zumkeller, Table of n, a(n) for n = 1..10001 %t A053754 Select[Range[0, 150], EvenQ @ IntegerLength[#, 2] &] (* _Amiram Eldar_, Feb 01 2021 *) %o A053754 (Haskell) %o A053754 a053754 n = a053754_list !! (n-1) %o A053754 a053754_list = 0 : filter (even . a070939) [1..] %o A053754 -- _Reinhard Zumkeller_, Apr 18 2015 %o A053754 (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 %o A053754 (PARI) a(n) = n-1 + (1<