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A003754
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Numbers with no 2 adjacent 0's in binary expansion.
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15
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0, 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 21, 22, 23, 26, 27, 29, 30, 31, 42, 43, 45, 46, 47, 53, 54, 55, 58, 59, 61, 62, 63, 85, 86, 87, 90, 91, 93, 94, 95, 106, 107, 109, 110, 111, 117, 118, 119, 122, 123, 125, 126, 127, 170, 171, 173, 174, 175, 181
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OFFSET
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1,3
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COMMENTS
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Theorem (J.-P. Allouche, J. Shallit, G. Skordev): This sequence = A052499 - 1.
A104326(n) = A007088(a(n)); A023416(a(n)) = A087116(a(n)); A107782(a(n)) = 0; A107345(a(n)) = 1; A107359(n) = a(n+1)-a(n); A104326(n) = A007088(a(n)); a(A001911(n)) = A000225(n); a(A000071(n+2)) = A000975(n). - Reinhard Zumkeller, May 25 2005
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REFERENCES
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David Garth and Adam Gouge, Affinely Self-Generating Sets and Morphisms, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.5.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
J.-P. Allouche, J. Shallit and G. Skordev, Self-generating sets, integers with missing blocks and substitutions, Discrete Math. 292 (2005) 1-15.
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MAPLE
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Contribution from R. J. Mathar, Oct 23 2010: (Start)
isA003754 := proc(n) local bdgs ; bdgs := convert(n, base, 2) ; for i from 2 to nops(bdgs) do if op(i, bdgs)=0 and op(i-1, bdgs)= 0 then return false; end if; end do; return true; end proc:
A003754 := proc(n) option remember; if n= 1 then 0; else for a from procname(n-1)+1 do if isA003754(a) then return a; end if; end do: end if; end proc: (End)
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MATHEMATICA
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Select[ Range[0, 200], !MatchQ[ IntegerDigits[#, 2], {___, 0, 0, ___}]&] (* From Jean-François Alcover, Oct 25 2011 *)
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PROG
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(Haskell)
a003754 n = a003754_list !! (n-1)
a003754_list = filter f [0..] where
f x = x == 0 || x `mod` 4 > 0 && f (x `div` 2)
-- Reinhard Zumkeller, Dec 07 2012, Oct 19 2011
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CROSSREFS
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Complement of A004753.
Cf. A023705.
Cf. A196168.
Sequence in context: A087007 A047586 A103841 * A087006 A144147 A068422
Adjacent sequences: A003751 A003752 A003753 * A003755 A003756 A003757
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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