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.

3, 6, 7, 10, 13, 14, 15, 18, 21, 22, 25, 28, 29, 30, 31, 34, 37, 38, 41, 44, 45, 46, 49, 52, 53, 56, 59, 60, 61, 62, 63, 66, 69, 70, 73, 76, 77, 78, 81, 84, 85, 88, 91, 92, 93, 94, 97, 100, 101, 104, 107, 108, 109, 112, 115, 116, 119, 122, 123, 124, 125, 126

Offset: 1

Author

N. J. A. Sloane and Benoit Cloitre, Apr 01 2003

Keywords

• nonn

Comments

It appears these are the indices of the terms in A182105 which are greater than 1. - Carl Joshua Quines, Apr 07 2017

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,3,1,3)-hiccup sequence. - Michael De Vlieger, Jul 30 2025

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..10000
• Benoit Cloitre, A study of a family of self-referential sequences, arXiv:2506.18103 [math.GM], 2025. See p. 15.
• Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
• Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.
• Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See p. 3.
• Geoffrey Powell, Symmetric powers, indecomposables and representation stability, arXiv:1809.08781 [math.AT], 2018.
• Frank Ruskey and Chris Deugau, The Combinatorics of Certain k-ary Meta-Fibonacci Sequences, JIS 12 (2009) 09.4.3.

Crossrefs

Cf. A080578.

Programs

Mathematica

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 *)

Python

l=[3]
a=3
for n in range(2, 101):
    if n not in l: a+=3
    else: a+=1
    l.append(a)
print(l) # Indranil Ghosh, Apr 07 2017