This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080579 #18 Jul 29 2025 16:15:07 %S A080579 1,5,9,13,14,18,22,26,27,31,35,39,40,41,45,49,53,54,58,62,66,67,71,75, %T A080579 79,80,81,85,89,93,94,98,102,106,107,111,115,119,120,121,122,126,130, %U A080579 134,135,139,143,147,148,152,156,160,161,162,166,170,174,175 %N A080579 a(1)=1; for n>1, a(n)=a(n-1)+1 if n is already in the sequence, a(n)=a(n-1)+4 otherwise. %C A080579 In the Fokkink-Joshi paper, this sequence is the Cloitre (0,1,1,4)-hiccup sequence. - _Michael De Vlieger_, Jul 29 2025 %H A080579 Reinhard Zumkeller, <a href="/A080579/b080579.txt">Table of n, a(n) for n = 1..10000</a> %H A080579 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 A080579 Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://arXiv.org/abs/math.NT/0305308">Numerical analogues of Aronson's sequence</a> (math.NT/0305308) %H A080579 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, 5. %t A080579 a[1] = 1; a[n_] := a[n] = If[MemberQ[Array[a, n-1], n], a[n-1]+1, a[n-1]+4]; Array[a, 60] (* _Jean-François Alcover_, Oct 08 2018 *) %o A080579 (Haskell) %o A080579 a080579 n = a080579_list !! (n-1) %o A080579 a080579_list = 1 : f 2 [1] where %o A080579 f x zs@(z:_) = y : f (x + 1) (y : zs) where %o A080579 y = if x `elem` zs then z + 1 else z + 4 %o A080579 -- _Reinhard Zumkeller_, Sep 26 2014 %Y A080579 Cf. A080455-A080458, A080036, A080037. %K A080579 nonn %O A080579 1,2 %A A080579 _N. J. A. Sloane_, Mar 23 2003