cp's OEIS Frontend

A081841 a(1)=0, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.

%I A081841 #17 Jul 29 2025 16:03:04
%S A081841 0,2,4,7,9,11,14,16,19,21,24,26,28,31,33,36,38,40,43,45,48,50,52,55,
%T A081841 57,60,62,65,67,69,72,74,77,79,81,84,86,89,91,94,96,98,101,103,106,
%U A081841 108,110,113,115,118,120,123,125,127,130,132,135,137,139,142,144,147,149,151
%N A081841 a(1)=0, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.
%C A081841 In the Fokkink-Joshi paper, this sequence is the Cloitre (0,0,3,2)-hiccup sequence. - _Michael De Vlieger_, Jul 29 2025
%H A081841 Michael De Vlieger, <a href="/A081841/b081841.txt">Table of n, a(n) for n = 1..10000</a>
%H A081841 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 A081841 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, 8.
%F A081841 a(1)=0; for n>=1 a(n)=floor(r*n-(4*r-1)/(r+1)) where r=1+sqrt(2)
%t A081841 Block[{c, k}, c[_] := False; k = 0; c[0] = True; {k}~Join~Reap[Do[If[c[n], k += 3, k += 2]; c[k] = True; Sow[k], {n, 2, 120}]][[-1, 1]] ] (* _Michael De Vlieger_, Jul 02 2025 *)
%Y A081841 Cf. A080353, A080580, A080590, A080600, A080652, A080754, A081834, A081840
%K A081841 nonn
%O A081841 1,2
%A A081841 _Benoit Cloitre_, Apr 11 2003