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A081839 a(1)=0, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

%I A081839 #15 Jul 29 2025 15:57:38
%S A081839 0,5,10,15,19,24,29,34,39,43,48,53,58,63,67,72,77,82,86,91,96,101,106,
%T A081839 110,115,120,125,130,134,139,144,149,154,158,163,168,173,178,182,187,
%U A081839 192,197,201,206,211,216,221,225,230,235,240,245,249,254,259,264,269
%N A081839 a(1)=0, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.
%C A081839 In the Fokkink-Joshi paper, this sequence is the Cloitre (0,0,4,5)-hiccup sequence. - _Michael De Vlieger_, Jul 29 2025
%H A081839 Michael De Vlieger, <a href="/A081839/b081839.txt">Table of n, a(n) for n = 1..10000</a>
%H A081839 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 A081839 a(n) = floor(r*n-(3*r+1)/(r-1)) where r = (1/2) *(5+sqrt(21)) = 4.79128784747792...
%t A081839 cloitreH[j_, x_, y_, z_, w_ : 120] := Module[{c, k}, c[_] := False; k = x; c[x] = True; {x}~Join~Reap[Do[If[c[n - j], k += y, k += z]; c[k] = True; Sow[k], {n, 2, w}] ][[-1, 1]] ]; cloitreH[0, 0, 4, 5] (* _Michael De Vlieger_, Jul 29 2025 *)
%Y A081839 Cf. A081834, A081835, A081840, A081841, A081842, A081843.
%K A081839 nonn
%O A081839 1,2
%A A081839 _Benoit Cloitre_, Apr 11 2003