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 A280873 Numbers whose binary expansion does not begin 10 and do not contain 2 adjacent 0's; Ahnentafel numbers of X-chromosome inheritance of a male. 5
 0, 1, 3, 6, 7, 13, 14, 15, 26, 27, 29, 30, 31, 53, 54, 55, 58, 59, 61, 62, 63, 106, 107, 109, 110, 111, 117, 118, 119, 122, 123, 125, 126, 127, 213, 214, 215, 218, 219, 221, 222, 223, 234, 235, 237, 238, 239, 245, 246, 247, 250, 251, 253, 254, 255 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The number of ancestors at generation n from whom a living individual may have received an X chromosome allele is Fn, the n-th term of the Fibonacci Sequence. From Antti Karttunen, Oct 11 2017: (Start) The starting offset is zero (with a(0) = 0) for the same reason that we have A003714(0) = 0. Indeed, b(n) = A054429(A003714(n)) for n >= 0 yields the terms of this sequence, but in different order. A163511(a(n)) for n >= 0 gives a permutation of squarefree numbers (A005117). See also A277006. (End) LINKS Antti Karttunen, Table of n, a(n) for n = 0..10946 David Eppstein, Self-recursive generators (Python recipe) L. A. D. Hutchison, N. M. Myres and S. R. Woodward, Growing the Family Tree: The Power of DNA in Reconstructing Family Relationships, Proceedings of the First Symposium on Bioinformatics and Biotechnology (BIOT-04, Colorado Springs), pp. 42-49, Sept. 2004. MAPLE gen[0]:= {0, 1, 3}: gen[1]:= {6, 7}: for n from 2 to 10 do   gen[n]:= map(t -> 2*t+1, gen[n-1]) union       map(t -> 2*t, select(type, gen[n-1], odd)) od: sort(convert(`union`(seq(gen[i], i=0..10)), list)); # Robert Israel, Oct 11 2017 MATHEMATICA male = {1, 3}; generations = 8; Do[x = male[[i - 1]]; If[EvenQ[x],                           male = Append[ male,   2*x + 1] ,                           male = Flatten[Append[male, {2*x, 2*x + 1}]]]        , {i, 3, Fibonacci[generations + 1]}]; male PROG (PARI) isA003754(n) = { n=bitor(n, n>>1)+1; n>>=valuation(n, 2); (n==1); }; \\ After Charles R Greathouse IV's Feb 06 2017 code. isA004760(n) = (n<2 || (binary(n)[2])); \\ This function also from Charles R Greathouse IV, Sep 23 2012 isA280873(n) = (isA003754(n) && isA004760(n)); n=0; k=0; while(k <= 10946, if(isA280873(n), write("b280873.txt", k, " ", n); k=k+1); n=n+1; ); \\ Antti Karttunen, Oct 11 2017 (Python) def A280873():     yield 1     for x in A280873():         if ((x & 1) and (x > 1)):             yield 2*x         yield 2*x+1 def take(n, g):   '''Returns a list composed of the next n elements returned by generator g.'''   z = []   if 0 == n: return(z)   for x in g:     z.append(x)     if n > 1: n = n-1     else: return(z) take(120, A280873()) # Antti Karttunen, Oct 11 2017, after the given Mathematica-code (by Floris Strijbos) and a similar generator-example for A003714 by David Eppstein (cf. "Self-recursive generators" link). CROSSREFS Cf. A003714, A054429. Intersection of A003754 and A004760. Positions where A163511 obtains squarefree (A005117) values. Cf. also A293437 (a subsequence). Sequence in context: A333002 A175048 A294231 * A293437 A282354 A088146 Adjacent sequences:  A280870 A280871 A280872 * A280874 A280875 A280876 KEYWORD nonn,base AUTHOR Floris Strijbos, Jan 09 2017 EXTENSIONS a(0) = 0 prepended and more descriptive alternative name added by Antti Karttunen, Oct 11 2017 STATUS approved

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)