%I A022340
%S A022340 0,2,4,8,10,16,18,20,32,34,36,40,42,64,66,68,72,74,80,82,84,128,130,132,
%T A022340 136,138,144,146,148,160,162,164,168,170,256,258,260,264,266,272,274,
%U A022340 276,288,290,292,296,298,320,322,324,328,330,336,338,340,512,514,516
%N A022340 Even Fibbinary numbers (A003714); also 2*Fibbinary(n).
%C A022340 Positions of ones in binomial(3k+2,k+1)/(3k+2) modulo 2 (A085405). - 
               Paul D. Hanna, (pauldhanna(AT)juno.com), Jun 29 2003.
%C A022340 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, 
               (pauldhanna(AT)juno.com), Jun 29 2003
%F A022340 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.
%F A022340 a(n) + a(n)/2 = a(n) XOR a(n)/2, see A106409. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 02 2005
%t A022340 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[ # ] &] (from Robert G. Wilson v 
               Sep 18 2004)
%Y A022340 Equals 2 * A003714.
%Y A022340 Cf. A006013, A001045, A085405, A085407.
%Y A022340 Sequence in context: A128106 A125021 A085406 this_sequence A093886 A125732 
               A032533
%Y A022340 Adjacent sequences: A022337 A022338 A022339 this_sequence A022341 A022342 
               A022343
%K A022340 nonn
%O A022340 0,2
%A A022340 Marc LeBrun (mlb(AT)well.com)
%E A022340 Edited by R. Stephan, Sep 01 2004