A086398 a(1)=1; a(n)=a(n-1)+2 if n is in the sequence; a(n)=a(n-1)+2 if n and (n-1) are not in the sequence; a(n)=a(n-1)+4 if n is not in the sequence but (n-1) is in the sequence.

1, 5, 7, 9, 11, 15, 17, 21, 23, 27, 29, 33, 35, 37, 39, 43, 45, 49, 51, 53, 55, 59, 61, 65, 67, 69, 71, 75, 77, 81, 83, 85, 87, 91, 93, 97, 99, 103, 105, 109, 111, 113, 115, 119, 121, 125, 127, 129, 131, 135, 137, 141, 143, 147, 149, 153, 155, 157, 159, 163, 165, 169

Offset: 1

Author

Benoit Cloitre, Sep 13 2003

Keywords

• nonn

Comments

Conjecture: the positions of 1 in the fixed point of the morphism 0 -> 10, 1 -> 1000, and -1 < n*(1 + sqrt(3)) - a(n) < 4 for n>=1; see A285301. - Clark Kimberling, Apr 25 2017

In the Fokkink-Joshi paper, this sequence is the Cloitre (1,1,4,2)-hiccup sequence. - Michael De Vlieger, Jul 29 2025

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000
• Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See pp. 2, 3, 5, 9, 12.

Crossrefs

Cf. A086377, A285301, A285302.

Programs

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {1, 0, 0, 0}}] &, {0}, 10]; (* A285301 *)
Flatten[Position[s, 0]];  (* A285302 *)
Flatten[Position[s, 1]];  (* A086398 *)

PARI

x=1; y=2; z=2; t=4; an[1]=x; for(n=2,100,an[n]=if(setsearch(Set(vector(n-1,i,a(i))),n),a(n-1)+y,if(setsearch(Set(vector(n-1,i,a(i))),n-1),a(n-1)+t,a(n-1)+z)))

Formula

a(n) = (1+sqrt(3))*n + O(1).