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Search: id:A022340
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| 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, 514, 516
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OFFSET
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0,2
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COMMENT
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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
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FORMULA
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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 (reinhard.zumkeller(AT)gmail.com), May 02 2005
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MATHEMATICA
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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)
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CROSSREFS
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Equals 2 * A003714.
Cf. A006013, A001045, A085405, A085407.
Adjacent sequences: A022337 A022338 A022339 this_sequence A022341 A022342 A022343
Sequence in context: A128106 A125021 A085406 this_sequence A093886 A125732 A032533
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KEYWORD
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nonn
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AUTHOR
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Marc LeBrun (mlb(AT)well.com)
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EXTENSIONS
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Edited by R. Stephan, Sep 01 2004
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