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 A062880 Zero together with numbers which can be written as a sum of distinct odd powers of 2. 19
 0, 2, 8, 10, 32, 34, 40, 42, 128, 130, 136, 138, 160, 162, 168, 170, 512, 514, 520, 522, 544, 546, 552, 554, 640, 642, 648, 650, 672, 674, 680, 682, 2048, 2050, 2056, 2058, 2080, 2082, 2088, 2090, 2176, 2178, 2184, 2186, 2208, 2210, 2216, 2218, 2560, 2562 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binary expansion of n does not contain 1-bits at even positions. Integers whose base-4 representation consists of only 0s and 2s. a(n)=2 A000695(n). Every nonnegative even number is a unique sum of the form a(k)+2a(l); moreover, this sequence is unique with such property. [Vladimir Shevelev, Nov 07 2008] Also numbers such that the digital sum base 2 and the digital sum base 4 are in a ratio of 2:4. - Michel Marcus, Sep 23 2013 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 D. H. Bailey, J. M. Borwein, R. E. Crandall, and C. Pomerance, On the binary expansions of algebraic numbers, J. Théor. Nombres Bordeaux, 16 (2004), 487-518. S. Eigen, A. Hajian, and S. Kalikow, Ergodic transformations and sequences of integers, Israel J. Math. 75 (1991), 119-128; Math. Rev. 1147294 (93c:28014). FORMULA From Robert Israel, Apr 10 2018: (Start) a(2*n) = 4*a(n). a(2*n+1) = 4*a(n)+2. G.f. g(x) satisfies: g(x) = 4*(1+x)*g(x^2)+2*x/(1-x^2). (End) MAPLE [seq(a(j), j=0..100)]; a := n -> add((floor(n/(2^i)) mod 2)*(2^((2*i)+1)), i=0..floor_log_2(n+1)); MATHEMATICA b[n_] := BitAnd[n, Sum[2^k, {k, 0, Log[2, n] // Floor, 2}]]; Select[Range[ 0, 10^4], b[#] == 0&] (* Jean-François Alcover, Feb 28 2016 *) PROG (Haskell) a062880 n = a062880_list !! n a062880_list = filter f [0..] where    f 0 = True    f x = (m == 0 || m == 2) && f x'  where (x', m) = divMod x 4 -- Reinhard Zumkeller, Nov 20 2012 CROSSREFS Except for first term, n such that A063694(n) = 0. Binary expansion is given in A062033. Interpreted as Zeckendorf expansion: A062879. A062880[n] = 2*A000695[n] Central diagonal of arrays A163357 and A163359. Sequence in context: A247592 A102943 A327988 * A066707 A107227 A188539 Adjacent sequences:  A062877 A062878 A062879 * A062881 A062882 A062883 KEYWORD nonn,easy AUTHOR Antti Karttunen, Jun 26 2001 STATUS approved

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Last modified April 3 03:42 EDT 2020. Contains 333195 sequences. (Running on oeis4.)