A080600 a(n) = ceiling(n*(3 + sqrt(13))/2).

0, 4, 7, 10, 14, 17, 20, 24, 27, 30, 34, 37, 40, 43, 47, 50, 53, 57, 60, 63, 67, 70, 73, 76, 80, 83, 86, 90, 93, 96, 100, 103, 106, 109, 113, 116, 119, 123, 126, 129, 133, 136, 139, 143, 146, 149, 152, 156, 159, 162, 166, 169, 172, 176, 179, 182, 185, 189

Offset

0,2

Comments

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

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

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Benoit Cloitre, A study of a family of self-referential sequences, arXiv:2506.18103 [math.GM], 2025. See p. 7.

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.

Mathematica

With[{c=(3+Sqrt[13])/2}, Table[Ceiling[c*n], {n, 0, 60}]] (* Harvey P. Dale, Oct 30 2021 *)

Crossrefs

Equals A080081 + 1 for n > 0. Cf. A080455-A080458, A080036, A080037.

Sequence in context: A310688 A062389 A191402 * A198266 A067497 A123384

Adjacent sequences: A080597 A080598 A080599 * A080601 A080602 A080603

Keyword

nonn

Author

N. J. A. Sloane, Mar 23 2003

Status

approved