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%I #13 Dec 02 2019 06:15:15
%S 1,5,7,9,11,15,17,21,23,27,29,33,35,37,39,43,45,49,51,53,55,59,61,65,
%T 67,69,71,75,77,81,83,85,87,91,93,97,99,103,105,109,111,113,115,119,
%U 121,125,127,129,131,135,137,141,143,147,149,153,155,157,159,163,165,169
%N a(1)=1; a(n)=a(n-1)+2 if n is in the sequence; a(n)=a(n-1)+2 if n and (n-1) are not in the sequence; a(n)=a(n-1)+4 if n is not in the sequence but (n-1) is in the sequence.
%C Conjecture: the positions of 1 in the fixed point of the morphism 0 -> 10, 1 -> 1000, and -1 < n*(1 + sqrt(3)) - a(n) < 4 for n>=1; see A285301. - _Clark Kimberling_, Apr 25 2017
%H Clark Kimberling, <a href="/A086398/b086398.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (1+sqrt(3))*n + O(1).
%t s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {1, 0, 0, 0}}] &, {0}, 10]; (* A285301 *)
%t Flatten[Position[s, 0]]; (* A285302 *)
%t Flatten[Position[s, 1]]; (* A086398 *)
%o (PARI) x=1; y=2; z=2; t=4; an[1]=x; for(n=2,100,an[n]=if(setsearch(Set(vector(n-1,i,a(i))),n),a(n-1)+y,if(setsearch(Set(vector(n-1,i,a(i))),n-1),a(n-1)+t,a(n-1)+z)))
%Y Cf. A086377, A285301, A285302.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Sep 13 2003
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