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 A081843 #21 Jul 29 2025 16:02:51
%S A081843 0,4,8,13,17,21,25,30,34,38,42,46,51,55,59,63,68,72,76,80,85,89,93,97,
%T A081843 102,106,110,114,118,123,127,131,135,140,144,148,152,157,161,165,169,
%U A081843 174,178,182,186,191,195,199,203,207,212,216,220,224,229,233,237,241
%N A081843 a(1)=0, a(n)=a(n-1)+5 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.
%C A081843 A high proportion of terms are the same as A004938, which is the nearest integer to n*r, where r=2+sqrt(5) as defined in the formula section. Allowing for the difference in offset, the first 3 terms to differ are those which have values 46, 63 and 118 instead of 47, 64 and 119. - _Peter Munn_, Aug 07 2019
%C A081843 In the Fokkink-Joshi paper, this sequence is the Cloitre (0,0,5,4)-hiccup sequence. - _Michael De Vlieger_, Jul 29 2025
%H A081843 Jinyuan Wang, <a href="/A081843/b081843.txt">Table of n, a(n) for n = 1..1000</a>
%H A081843 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 A081843 a(n) = floor(r*n-(5*r-1)/(r+1)) where r=2+sqrt(5).
%t A081843 Clear[used];used={}; nxt[{n_,a_}]:=Module[{c=If[MemberQ[ used,n+1],5,4]},Flatten[ AppendTo[ used,a+c]];{n+1,c+a}]; NestList[nxt,{1,0},60][[All,2]] (* _Harvey P. Dale_, Aug 16 2021 *)
%Y A081843 Cf. A004938, A081835, A081839.
%K A081843 nonn
%O A081843 1,2
%A A081843 _Benoit Cloitre_, Apr 11 2003