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 A003754 Numbers with no 2 adjacent 0's in binary expansion. 27
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Theorem (J.-P. Allouche, J. Shallit, G. Skordev): This sequence = A052499 - 1. Ahnentafel numbers of ancestors contributing the X-chromosome to a female. A280873 gives the male inheritance. - Floris Strijbos, Jan 09 2017 [Equivalence with this sequence pointed out by John Blythe Dobson, May 09 2018] LINKS Indranil Ghosh, Table of n, a(n) for n = 1..50000 (terms 1..1000 from T. D. Noe) J.-P. Allouche, J. Shallit and G. Skordev, Self-generating sets, integers with missing blocks and substitutions, Discrete Math. 292 (2005) 1-15. David Garth and Adam Gouge, Affinely Self-Generating Sets and Morphisms, Journal of Integer Sequences, Article 07.1.5, 10 (2007) 1-13. T. Karki, A. Lacroix, M. Rigo, On the recognizability of self-generating sets, JIS 13 (2010) #10.2.2. Wikipedia, Ahnentafel EXAMPLE 21 is in the sequence because 21 = 10101_2. '10101' has no '00' present in it. - Indranil Ghosh, Feb 11 2017 MAPLE 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: # R. J. Mathar, Oct 23 2010 MATHEMATICA Select[ Range[0, 200], !MatchQ[ IntegerDigits[#, 2], {___, 0, 0, ___}]&] (* Jean-François Alcover, Oct 25 2011 *) Select[Range[0, 200], SequenceCount[IntegerDigits[#, 2], {0, 0}]==0&] (* The program uses the SequenceCount function from Mathematica version 10 *) (* Harvey P. Dale, May 21 2015 *) PROG (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 (PARI) is(n)=n=bitor(n, n>>1)+1; n>>=valuation(n, 2); n==1 \\ Charles R Greathouse IV, Feb 06 2017 (Python) i=0 j=1 while j<=50000: ....if bin(i)[2:].count("00")==0: ........print str(j)+" "+str(i) ........j+=1 ....i+=1 # Indranil Ghosh, Feb 11 2017 CROSSREFS 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 Cf. A003796 (no 000), A004745 (no 001), A004746 (no 010), A004744 (no 011), A004742 (no 101), A004743 (no 110), A003726 (no 111). Complement of A004753. Cf. A023705, A196168, A280873. Sequence in context: A087007 A047586 A103841 * A293427 A293430 A087006 Adjacent sequences:  A003751 A003752 A003753 * A003755 A003756 A003757 KEYWORD nonn,easy,base,nice AUTHOR STATUS approved

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Last modified October 14 07:31 EDT 2019. Contains 327995 sequences. (Running on oeis4.)