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 A022340 Even Fibbinary numbers (A003714); also 2*Fibbinary(n). 9
 0, 2, 4, 8, 10, 16, 18, 20, 32, 34, 36, 40, 42, 64, 66, 68, 72, 74, 80, 82, 84, 128, 130, 132, 136, 138, 144, 146, 148, 160, 162, 164, 168, 170, 256, 258, 260, 264, 266, 272, 274, 276, 288, 290, 292, 296, 298, 320, 322, 324, 328, 330, 336, 338, 340, 512 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Positions of ones in binomial(3k+2,k+1)/(3k+2) modulo 2 (A085405). - Paul D. Hanna, Jun 29 2003 Construction: start with strings S(0)={0}, S(1)={2}; for k>=2, concatenate all prior strings excluding S(k-1) and add 2^k to each element in the resulting string to obtain S(k); this sequence is the concatenation of all such generated strings: {S(0),S(1),S(2),...}. Example: for k=5, concatenate {S(0),S(1),S(2),S(3)} = {0, 2, 4, 8,10}; add 2^5 to each element to obtain S(5)={32,34,38,40,42}. - Paul D. Hanna, Jun 29 2003 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA For n>0, a(F(n))=2^n, a(F(n)-1)=A001045(n+2)-1, where F(n) is the n-th Fibonacci number with F(0)=F(1)=1. a(n) + a(n)/2 = a(n) XOR a(n)/2, see A106409. - Reinhard Zumkeller, May 02 2005 MATHEMATICA f[n_Integer] := Block[{k = Ceiling[ Log[ GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[fr, 1]; t = t - Fibonacci[k], AppendTo[fr, 0]]; k-- ]; FromDigits[fr, 2]]; Select[f /@ Range[0, 95], EvenQ[ # ] &] (* Robert G. Wilson v, Sep 18 2004 *) Select[Range[2, 512, 2], BitAnd[#, 2#] == 0 &] (* Alonso del Arte, Jun 18 2012 *) PROG (Haskell) a022340 = (* 2) . a003714 -- Reinhard Zumkeller, Feb 03 2015 CROSSREFS Equals 2 * A003714. Cf. A006013, A001045, A085405, A085407. Sequence in context: A128106 A125021 A085406 * A093886 A125732 A032533 Adjacent sequences:  A022337 A022338 A022339 * A022341 A022342 A022343 KEYWORD nonn AUTHOR EXTENSIONS Edited by Ralf Stephan, Sep 01 2004 STATUS approved

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