A080579 a(1)=1; for n>1, a(n)=a(n-1)+1 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.

1, 5, 9, 13, 14, 18, 22, 26, 27, 31, 35, 39, 40, 41, 45, 49, 53, 54, 58, 62, 66, 67, 71, 75, 79, 80, 81, 85, 89, 93, 94, 98, 102, 106, 107, 111, 115, 119, 120, 121, 122, 126, 130, 134, 135, 139, 143, 147, 148, 152, 156, 160, 161, 162, 166, 170, 174, 175

Offset: 1

Author

N. J. A. Sloane, Mar 23 2003

Keywords

• nonn

Comments

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• 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 (math.NT/0305308)
• Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See pp. 3, 5.

Crossrefs

Cf. A080455-A080458, A080036, A080037.

Programs

Haskell

a080579 n = a080579_list !! (n-1)
a080579_list = 1 : f 2 [1] where
   f x zs@(z:_) = y : f (x + 1) (y : zs) where
     y = if x `elem` zs then z + 1 else z + 4
-- Reinhard Zumkeller, Sep 26 2014

Mathematica

a[1] = 1; a[n_] := a[n] = If[MemberQ[Array[a, n-1], n], a[n-1]+1, a[n-1]+4]; Array[a, 60] (* Jean-François Alcover, Oct 08 2018 *)