A280873 Numbers whose binary expansion does not begin 10 and does not contain 2 adjacent 0's; Ahnentafel numbers of X-chromosome inheritance of a male.
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
Offset: 0
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.
- Index entries for sequences related to binary expansion of n
Crossrefs
Programs
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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 -
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
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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).
Formula
Extensions
a(0) = 0 prepended and more descriptive alternative name added by Antti Karttunen, Oct 11 2017
Comments