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

1,2

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, Ramanujan J. 69 (2026), 40. See pp. 2, 4 (Table 1), 5, 9, 14 (Lemma 14). See also arXiv:2507.16956 [math.CO], 2025. See pp. 2, 3, 5, 9, 12.

Formula

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

a(n) = A284753(n) - 1. [Fokkink-Joshi] - Michael De Vlieger, Feb 02 2026

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 *)

Prog

(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)))

Crossrefs

Cf. A086377, A285301, A285302, A284753.

Sequence in context: A314375 A309747 A080384 * A356052 A023380 A076190

Adjacent sequences: A086395 A086396 A086397 * A086399 A086400 A086401

Keyword

nonn

Author

Benoit Cloitre, Sep 13 2003

Status

approved