cp's OEIS Frontend

A086398 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.

%I A086398 #17 Jul 29 2025 16:02:55
%S A086398 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 A086398 67,69,71,75,77,81,83,85,87,91,93,97,99,103,105,109,111,113,115,119,
%U A086398 121,125,127,129,131,135,137,141,143,147,149,153,155,157,159,163,165,169
%N A086398 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 A086398 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
%C A086398 In the Fokkink-Joshi paper, this sequence is the Cloitre (1,1,4,2)-hiccup sequence. - _Michael De Vlieger_, Jul 29 2025
%H A086398 Clark Kimberling, <a href="/A086398/b086398.txt">Table of n, a(n) for n = 1..10000</a>
%H A086398 Robbert Fokkink and Gandhar Joshi, <a href="https://arxiv.org/abs/2507.16956">On Cloitre's hiccup sequences</a>, arXiv:2507.16956 [math.CO], 2025. See pp. 2, 3, 5, 9, 12.
%F A086398 a(n) = (1+sqrt(3))*n + O(1).
%t A086398 s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {1, 0, 0, 0}}] &, {0}, 10]; (* A285301 *)
%t A086398 Flatten[Position[s, 0]];  (* A285302 *)
%t A086398 Flatten[Position[s, 1]];  (* A086398 *)
%o A086398 (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 A086398 Cf. A086377, A285301, A285302.
%K A086398 nonn
%O A086398 1,2
%A A086398 _Benoit Cloitre_, Sep 13 2003