A081839 a(1)=0, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

0, 5, 10, 15, 19, 24, 29, 34, 39, 43, 48, 53, 58, 63, 67, 72, 77, 82, 86, 91, 96, 101, 106, 110, 115, 120, 125, 130, 134, 139, 144, 149, 154, 158, 163, 168, 173, 178, 182, 187, 192, 197, 201, 206, 211, 216, 221, 225, 230, 235, 240, 245, 249, 254, 259, 264, 269

Offset

1,2

Comments

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,0,4,5)-hiccup sequence. - Michael De Vlieger, Jul 29 2025

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

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(r*n-(3*r+1)/(r-1)) where r = (1/2) *(5+sqrt(21)) = 4.79128784747792...

Mathematica

cloitreH[j_, x_, y_, z_, w_ : 120] := Module[{c, k}, c[_] := False; k = x; c[x] = True; {x}~Join~Reap[Do[If[c[n - j], k += y, k += z]; c[k] = True; Sow[k], {n, 2, w}] ][[-1, 1]] ]; cloitreH[0, 0, 4, 5] (* Michael De Vlieger, Jul 29 2025 *)

Crossrefs

Cf. A081834, A081835, A081840, A081841, A081842, A081843.

Sequence in context: A313690 A313691 A313692 * A313693 A313694 A313695

Adjacent sequences: A081836 A081837 A081838 * A081840 A081841 A081842

Keyword

nonn

Author

Benoit Cloitre, Apr 11 2003

Status

approved