A080667 a(1)=3; for n>1, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.

3, 6, 10, 13, 16, 20, 23, 26, 29, 33, 36, 39, 43, 46, 49, 53, 56, 59, 62, 66, 69, 72, 76, 79, 82, 86, 89, 92, 96, 99, 102, 105, 109, 112, 115, 119, 122, 125, 129, 132, 135, 138, 142, 145, 148, 152, 155, 158, 162, 165, 168, 171, 175, 178, 181, 185, 188

Offset

1,1

Comments

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,3,4,3)-hiccup sequence. - Michael De Vlieger, Jul 29 2025

Links

Table of n, a(n) for n=1..57.

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, Ramanujan J. 69 (2026), 40. See p. 4, Table 1. See also arXiv:2507.16956 [math.CO], 2025. See p. 3.

Formula

a(n) = floor(n*r + 1/(1+r)) where r = (3 + sqrt(13))/2.

Mathematica

a[1] = 3; a[n_] := a[n] = a[n-1] + If[MemberQ[Array[a, n-1], n], 4, 3];
Array[a, 60] (* Jean-François Alcover, Nov 25 2018 *)

Crossrefs

Cf. A080455, A080456, A080457, A080458, A080036, A080037.

Sequence in context: A028433 A310051 A353093 * A277722 A190007 A310052

Adjacent sequences: A080664 A080665 A080666 * A080668 A080669 A080670

Keyword

nonn

Author

N. J. A. Sloane, Mar 23 2003

Status

approved