A081842 a(1)=0, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.

0, 3, 7, 10, 13, 16, 20, 23, 26, 30, 33, 36, 40, 43, 46, 50, 53, 56, 59, 63, 66, 69, 73, 76, 79, 83, 86, 89, 92, 96, 99, 102, 106, 109, 112, 116, 119, 122, 125, 129, 132, 135, 139, 142, 145, 149, 152, 155, 158, 162, 165, 168, 172, 175, 178, 182, 185, 188, 192, 195

Offset

1,2

Comments

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

Links

Michael De Vlieger, 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. 7.

Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, Ramanujan J. 69 (2026), 40. See p. 3. See also arXiv:2507.16956 [math.CO], 2025. See p. 3.

Formula

a(n) = floor(r*n-(4*r-1)/(r+1)) where r = (1/2)*(3+sqrt(13)).

Mathematica

Module[{seq={0}, n=2}, Do[If[MemberQ[seq, n], AppendTo[seq, Last[seq]+4], AppendTo[seq, Last[seq]+3]]; n++, {60}]; seq] (* Harvey P. Dale, Nov 20 2012 *)

Crossrefs

Cf. A080353, A080580, A080590, A080600, A080652, A080754, A081834, A081840, A081841.

Sequence in context: A370756 A226723 A029918 * A160591 A297466 A198267

Adjacent sequences: A081839 A081840 A081841 * A081843 A081844 A081845

Keyword

nonn

Author

Benoit Cloitre, Apr 11 2003

Status

approved