A191109 a(1)=1, and if x is a term then 3x-1 and 3x+2 are terms too.

1, 2, 5, 8, 14, 17, 23, 26, 41, 44, 50, 53, 68, 71, 77, 80, 122, 125, 131, 134, 149, 152, 158, 161, 203, 206, 212, 215, 230, 233, 239, 242, 365, 368, 374, 377, 392, 395, 401, 404, 446, 449, 455, 458, 473, 476, 482, 485, 608, 611, 617, 620, 635, 638, 644, 647, 689, 692, 698, 701, 716, 719, 725, 728, 1094, 1097, 1103, 1106, 1121

Offset: 1

Author

Clark Kimberling, May 26 2011

Keywords

• nonn

Comments

See discussions at A190803, A191106.

The positive integers in (1+A191109)/3 comprise A153775, a proper subsequence of A191109.

The positive integers in (-2+A191109)/3 comprise A032924, a proper subsequence of A191109.

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Juha Honkala, On number systems with negative digits, Annales Academiae Scientiarum Fennicae, Series A. I. Mathematica, Vol. 14, 1989, pp. 149-156.

Crossrefs

Cf. A190803, A191106, A153775, A032924.

Programs

Mathematica

h = 3; i = -1; j = 3; k = 2; f = 1;  g = 7;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* 191109 *)
b = (a + 1)/3; c = (a - 2)/3; r = Range[1, 900];
d = Intersection[b, r] (* A153775 *)
e = Intersection[c, r] (* A032924 *)
Nest[Flatten[{#,3#-1,3#+2}]&,1,10]//Union (* Harvey P. Dale, Apr 05 2020 *)

Extensions

Name edited by Michel Marcus, Jul 29 2021