A080590 a(1)=1; for n>1, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.

1, 5, 9, 13, 16, 20, 24, 28, 31, 35, 39, 43, 46, 50, 54, 57, 61, 65, 69, 72, 76, 80, 84, 87, 91, 95, 99, 102, 106, 110, 113, 117, 121, 125, 128, 132, 136, 140, 143, 147, 151, 155, 158, 162, 166, 169, 173, 177, 181, 184, 188, 192, 196, 199, 203, 207

Offset

1,2

Comments

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,1,3,4)-hiccup sequence. - Michael De Vlieger, Jul 29 2025

Links

Reinhard Zumkeller, 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. 9.

Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.

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.

Mathematica

a[n_] := a[n] = If[n == 1, 1, If[MemberQ[Array[a, n-1], n], a[n-1]+3, a[n-1]+4]]; Array[a, 56] (* Jean-François Alcover, Oct 05 2018 *)

Prog

(Haskell)
a080590 n = a080590_list !! (n-1)
a080590_list = 1 : f 2 [1] where
   f x zs@(z:_) = y : f (x + 1) (y : zs) where
     y = z + (if x `elem` zs then 3 else 4)
-- Reinhard Zumkeller, Sep 26 2014

Crossrefs

Cf. A003151, A080455-A080458, A080036, A080037.

Cf. A081834.

Sequence in context: A227118 A314661 A316838 * A281582 A190696 A314662

Adjacent sequences: A080587 A080588 A080589 * A080591 A080592 A080593

Keyword

nonn

Author

N. J. A. Sloane, Mar 23 2003

Status

approved