

A280873


Numbers whose binary expansion does not begin 10 and do not contain 2 adjacent 0's; Ahnentafel numbers of Xchromosome 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
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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 nth 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, Selfrecursive 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 (BIOT04, Colorado Springs), pp. 4249, Sept. 2004.
Index entries for sequences related to binary expansion of n


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[n1]) union
map(t > 2*t, select(type, gen[n1], 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 = n1
else: return(z)
take(120, A280873())
# Antti Karttunen, Oct 11 2017, after the given Mathematicacode (by Floris Strijbos) and a similar generatorexample for A003714 by David Eppstein (cf. "Selfrecursive 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



