cp's OEIS Frontend

A080590 a(1)=1; for n>1, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.

%I A080590 #28 Jul 29 2025 16:15:29
%S A080590 1,5,9,13,16,20,24,28,31,35,39,43,46,50,54,57,61,65,69,72,76,80,84,87,
%T A080590 91,95,99,102,106,110,113,117,121,125,128,132,136,140,143,147,151,155,
%U A080590 158,162,166,169,173,177,181,184,188,192,196,199,203,207
%N A080590 a(1)=1; for n>1, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.
%C A080590 In the Fokkink-Joshi paper, this sequence is the Cloitre (0,1,3,4)-hiccup sequence. - _Michael De Vlieger_, Jul 29 2025
%H A080590 Reinhard Zumkeller, <a href="/A080590/b080590.txt">Table of n, a(n) for n = 1..10000</a>
%H A080590 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. 9.
%H A080590 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 A080590 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 A080590 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.
%t A080590 a[n_] := a[n] = If[n == 1, 1, If[MemberQ[Array[a, n-1], n], a[n-1]+3, a[n-1]+4]]; Array[a, 56] (* _Jean-François Alcover_, Oct 05 2018 *)
%o A080590 (Haskell)
%o A080590 a080590 n = a080590_list !! (n-1)
%o A080590 a080590_list = 1 : f 2 [1] where
%o A080590    f x zs@(z:_) = y : f (x + 1) (y : zs) where
%o A080590      y = z + (if x `elem` zs then 3 else 4)
%o A080590 -- _Reinhard Zumkeller_, Sep 26 2014
%Y A080590 Cf. A003151, A080455-A080458, A080036, A080037.
%Y A080590 Cf. A081834.
%K A080590 nonn
%O A080590 1,2
%A A080590 _N. J. A. Sloane_, Mar 23 2003