cp's OEIS Frontend

A081840 a(1)=0, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.

%I A081840 #19 Jul 29 2025 16:03:07
%S A081840 0,4,8,11,15,19,23,26,30,34,37,41,45,49,52,56,60,64,67,71,75,79,82,86,
%T A081840 90,93,97,101,105,108,112,116,120,123,127,131,134,138,142,146,149,153,
%U A081840 157,161,164,168,172,176,179,183,187,190,194,198,202,205,209,213,217
%N A081840 a(1)=0, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.
%C A081840 In the Fokkink-Joshi paper, this sequence is the Cloitre (0,0,3,4)-hiccup sequence. - _Michael De Vlieger_, Jul 29 2025
%H A081840 Michael De Vlieger, <a href="/A081840/b081840.txt">Table of n, a(n) for n = 1..10000</a>
%H A081840 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 A081840 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 A081840 a(n) = floor(r*n-(2*r+1)/(r-1)) where r = 2+sqrt(3).
%t A081840 Block[{c, k}, c[_] := False; k = 0; c[0] = True; {k}~Join~Reap[Do[If[c[n], k += 3, k += 4]; c[k] = True; Sow[k], {n, 2, 120}]][[-1, 1]] ] (* _Michael De Vlieger_, Jul 02 2025 *)
%Y A081840 Cf. A080353, A080580, A080590, A080600, A080652, A080754, A081834.
%K A081840 nonn
%O A081840 1,2
%A A081840 _Benoit Cloitre_, Apr 11 2003