cp's OEIS Frontend

A080667 a(1)=3; for n>1, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.

%I A080667 #19 Jul 29 2025 16:15:58
%S A080667 3,6,10,13,16,20,23,26,29,33,36,39,43,46,49,53,56,59,62,66,69,72,76,
%T A080667 79,82,86,89,92,96,99,102,105,109,112,115,119,122,125,129,132,135,138,
%U A080667 142,145,148,152,155,158,162,165,168,171,175,178,181,185,188
%N A080667 a(1)=3; for n>1, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.
%C A080667 In the Fokkink-Joshi paper, this sequence is the Cloitre (0,3,4,3)-hiccup sequence. - _Michael De Vlieger_, Jul 29 2025
%H A080667 Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
%H A080667 Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="https://arxiv.org/abs/math/0305308">Numerical analogues of Aronson's sequence</a>, arXiv:math/0305308 [math.NT], 2003.
%H A080667 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 p. 3.
%F A080667 a(n) = floor(n*r + 1/(1+r)) where r = (3 + sqrt(13))/2.
%t A080667 a[1] = 3; a[n_] := a[n] = a[n-1] + If[MemberQ[Array[a, n-1], n], 4, 3];
%t A080667 Array[a, 60] (* _Jean-François Alcover_, Nov 25 2018 *)
%Y A080667 Cf. A080455, A080456, A080457, A080458, A080036, A080037.
%K A080667 nonn
%O A080667 1,1
%A A080667 _N. J. A. Sloane_, Mar 23 2003