A081840 a(1)=0, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.

0, 4, 8, 11, 15, 19, 23, 26, 30, 34, 37, 41, 45, 49, 52, 56, 60, 64, 67, 71, 75, 79, 82, 86, 90, 93, 97, 101, 105, 108, 112, 116, 120, 123, 127, 131, 134, 138, 142, 146, 149, 153, 157, 161, 164, 168, 172, 176, 179, 183, 187, 190, 194, 198, 202, 205, 209, 213, 217

Offset

1,2

Comments

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

Links

Michael De Vlieger, 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.

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(r*n-(2*r+1)/(r-1)) where r = 2+sqrt(3).

Mathematica

Block[{c, k}, c[_] := False; k = 0; c[0] = True; {k}~Join~Reap[Do[If[c[n], k += 3, k += 4]; c[k] = True; Sow[k], {n, 2, 120}]][[-1, 1]] ] (* Michael De Vlieger, Jul 02 2025 *)

Crossrefs

Cf. A080353, A080580, A080590, A080600, A080652, A080754, A081834.

Sequence in context: A047346 A198270 A214971 * A311050 A311051 A311052

Adjacent sequences: A081837 A081838 A081839 * A081841 A081842 A081843

Keyword

nonn

Author

Benoit Cloitre, Apr 11 2003

Status

approved