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A022340 Even Fibbinary numbers (A003714); also 2*Fibbinary(n). 8
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, (pauldhanna(AT)juno.com), 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, (pauldhanna(AT)juno.com), Jun 29 2003

LINKS

Table of n, a(n) for n=0..55.

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[ # ] &] (* from Robert G. Wilson v Sep 18 2004 *)

Select[Range[2, 512, 2], BitAnd[#, 2#] == 0 &] (* Alonso del Arte, Jun 18 2012 *)

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

Marc LeBrun

EXTENSIONS

Edited by Ralf Stephan, Sep 01 2004

STATUS

approved

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Last modified April 16 00:25 EDT 2014. Contains 240534 sequences.