cp's OEIS Frontend

A045412 a(1)=3; for n > 1, a(n) = a(n-1) + 1 if n is already in the sequence, a(n) = a(n-1) + 3 otherwise.

%I A045412 #45 Jul 30 2025 17:48:35
%S A045412 3,6,7,10,13,14,15,18,21,22,25,28,29,30,31,34,37,38,41,44,45,46,49,52,
%T A045412 53,56,59,60,61,62,63,66,69,70,73,76,77,78,81,84,85,88,91,92,93,94,97,
%U A045412 100,101,104,107,108,109,112,115,116,119,122,123,124,125,126
%N A045412 a(1)=3; for n > 1, a(n) = a(n-1) + 1 if n is already in the sequence, a(n) = a(n-1) + 3 otherwise.
%C A045412 It appears these are the indices of the terms in A182105 which are greater than 1. - _Carl Joshua Quines_, Apr 07 2017
%C A045412 In the Fokkink-Joshi paper, this sequence is the Cloitre (0,3,1,3)-hiccup sequence. - _Michael De Vlieger_, Jul 30 2025
%H A045412 Indranil Ghosh, <a href="/A045412/b045412.txt">Table of n, a(n) for n = 1..10000</a>
%H A045412 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. 15.
%H A045412 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 A045412 Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="https://arxiv.org/abs/math/0305308">Numerical analogues of Aronson's sequence</a>, arXiv:math/0305308 [math.NT], 2003.
%H A045412 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.
%H A045412 Geoffrey Powell, <a href="https://arxiv.org/abs/1809.08781">Symmetric powers, indecomposables and representation stability</a>, arXiv:1809.08781 [math.AT], 2018.
%H A045412 Frank Ruskey and Chris Deugau, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Ruskey/ruskey6.html">The Combinatorics of Certain k-ary Meta-Fibonacci Sequences</a>, JIS 12 (2009) 09.4.3.
%t A045412 l={3}; a=3; For[n=2, n<=100, If[MemberQ[l, n], a=a+1, a=a+3]; AppendTo[l, a]; n++]; l (* _Indranil Ghosh_, Apr 07 2017 *)
%o A045412 (Python)
%o A045412 l=[3]
%o A045412 a=3
%o A045412 for n in range(2, 101):
%o A045412     if n not in l: a+=3
%o A045412     else: a+=1
%o A045412     l.append(a)
%o A045412 print(l) # _Indranil Ghosh_, Apr 07 2017
%Y A045412 Cf. A080578.
%K A045412 nonn
%O A045412 1,1
%A A045412 _N. J. A. Sloane_ and _Benoit Cloitre_, Apr 01 2003