A081835 a(1)=1, a(n) = a(n-1) + 5 if n is already in the sequence, a(n) = a(n-1) + 4 otherwise.

1, 5, 9, 13, 18, 22, 26, 30, 35, 39, 43, 47, 52, 56, 60, 64, 68, 73, 77, 81, 85, 90, 94, 98, 102, 107, 111, 115, 119, 124, 128, 132, 136, 140, 145, 149, 153, 157, 162, 166, 170, 174, 179, 183, 187, 191, 196, 200, 204, 208, 212, 217, 221, 225, 229, 234, 238, 242

Offset: 1

Author

Benoit Cloitre, Apr 11 2003

Keywords

• nonn

Comments

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,1,5,4)-hiccup sequence. - Michael De Vlieger, Jul 29 2025

Examples

			a(2) = a(1)+4 = 5 because 2 is not already in the sequence;
a(3) = a(2)+4 = 9 because 3 is not already in the sequence;
a(4) = a(3)+4 = 13 because 4 is not already in the sequence;
a(5) = a(4)+5 = 18 because 5 is already in the sequence.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..2000
• Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See p. 3.

Crossrefs

Cf. A064437, A081843.

Programs

Maple

r:=2+sqrt(5): seq(floor(r*n-(4*r-1)/(r+1)),n=1..60); # Muniru A Asiru, Jun 06 2018

Mathematica

Module[{r=2+Sqrt[5],c},c=(4r-1)/(r+1);Table[Floor[r*n-c],{n,60}]] (* Harvey P. Dale, Feb 19 2013 *)

Formula

a(n) = floor(rn-(4r-1)/(r+1)) where r=2+sqrt(5).