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A080652 a(1)=2; for n>1, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.

%I A080652 #27 Jul 29 2025 16:15:18
%S A080652 2,5,7,9,12,14,17,19,22,24,26,29,31,34,36,38,41,43,46,48,50,53,55,58,
%T A080652 60,63,65,67,70,72,75,77,79,82,84,87,89,92,94,96,99,101,104,106,108,
%U A080652 111,113,116,118,121,123,125,128,130,133,135,137,140,142,145
%N A080652 a(1)=2; for n>1, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.
%C A080652 In the Fokkink-Joshi paper, this sequence is the Cloitre (0,2,3,2)-hiccup sequence. - _Michael De Vlieger_, Jul 29 2025
%H A080652 Vincenzo Librandi, <a href="/A080652/b080652.txt">Table of n, a(n) for n = 1..5000</a>
%H A080652 Benoit Cloitre, <a href="https://arxiv.org/abs/2506.18103">A study of a family of self-referential sequences</a>, arXiv:2506.18103 [math.GM], 2025. See p. 7.
%H A080652 Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="https://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 A080652 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 A080652 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. 3, 9.
%F A080652 a(n) = floor(n*r + 1/(1+r)) where r = 1+sqrt(2).
%t A080652 a[1] = 2;
%t A080652 a[n_] := a[n] = If[MemberQ[Array[a, n-1], n], a[n-1] + 3, a[n-1] + 2];
%t A080652 Array[a, 60] (* _Jean-François Alcover_, Oct 01 2018 *)
%t A080652 Table[Floor[n (1 + Sqrt[2]) + 1 / (1 + (1 + Sqrt[2]))], {n, 60}] (* _Vincenzo Librandi_, Oct 02 2018 *)
%o A080652 (PARI) a(n) = my(r=sqrt(2)+1); (r*(r+1)*n+1)\(r+1); \\ _Altug Alkan_, Oct 01 2018
%o A080652 (Magma) [Floor(n*(1+Sqrt(2)) + 1/(1+(1+Sqrt(2)))): n in [1..60]]; // _Vincenzo Librandi_, Oct 02 2018
%Y A080652 Cf. A080455-A080458, A080036, A080037. Apart from start, equals A064437 - 1.
%K A080652 nonn
%O A080652 1,1
%A A080652 _N. J. A. Sloane_, Mar 23 2003