A081834 a(1)=1, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.

1, 4, 7, 11, 14, 17, 21, 24, 27, 30, 34, 37, 40, 44, 47, 50, 54, 57, 60, 63, 67, 70, 73, 77, 80, 83, 87, 90, 93, 97, 100, 103, 106, 110, 113, 116, 120, 123, 126, 130, 133, 136, 139, 143, 146, 149, 153, 156, 159, 163, 166, 169, 172, 176, 179, 182, 186, 189, 192, 196

Offset

1,2

Comments

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,1,4,3)-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. 7.

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.

Formula

a(n) = floor(rn-(3r-1)/(r+1)) where r = (1/2) *(3+sqrt(13)).

Mathematica

Block[{c, k, nn}, nn = 10^4; c[_] := False; k = 1; c[1] = True; {k}~Join~Reap[Do[If[c[n], k += 4, k += 3]; c[k] = True; Sow[k], {n, 2, nn}] ][[-1, 1]] ] (* Michael De Vlieger, Jul 02 2025 *)

Prog

(Haskell)
a081834 n = a081834_list !! (n-1)
a081834_list = 1 : f 2 [1] where
   f x zs@(z:_) = y : f (x + 1) (y : zs) where
     y = z + (if x `elem` zs then 4 else 3)
-- Reinhard Zumkeller, Sep 26 2014

Crossrefs

Cf. A064437, A080590, A080600, A080667, A081842.

Sequence in context: A212447 A172513 A327737 * A078309 A195171 A184623

Adjacent sequences: A081831 A081832 A081833 * A081835 A081836 A081837

Keyword

nonn

Author

Benoit Cloitre, Apr 11 2003

Status

approved