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A286031
Positions of 1 in A285568; complement of A285569.
3
1, 2, 4, 5, 8, 9, 11, 12, 13, 14, 16, 17, 20, 21, 23, 24, 26, 27, 30, 31, 33, 34, 36, 37, 40, 41, 43, 44, 45, 46, 48, 49, 52, 53, 55, 56, 58, 59, 62, 63, 66, 67, 70, 71, 73, 74, 76, 77, 80, 81, 83, 84, 85, 86, 88, 89, 92, 93, 95, 96, 98, 99, 102, 103, 105
OFFSET
1,2
COMMENTS
Conjecture: a(n)/n -> (1+sqrt(5))/2 = golden ratio (A001622).
Proof of this conjecture: the limit is 1/f0 where f0 is the frequency of 0 in (a(n)). Since the generating morphism of (a(n)) has the same incidence matrix as the generating morphism 0->11, 1->0101 of the sequence A285518, it follows that 1/f0 = phi = golden ratio. - Michel Dekking, Feb 22 2021
LINKS
EXAMPLE
As a word, A285568 = 110110011011..., in which 1 is in positions 1,2,4,5,8,...
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 1, 1, 0}}] &, {0}, 9] (* A285568 *)
Flatten[Position[s, 0]] (* A285569 *)
Flatten[Position[s, 1]] (* A286031 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 30 2017
STATUS
approved