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

1,2

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.

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 *)

Crossrefs

Cf. A190803, A191106, A153775, A032924.

Sequence in context: A202273 A210702 A173177 * A190105 A295400 A266287

Adjacent sequences: A191106 A191107 A191108 * A191110 A191111 A191112

Keyword

nonn

Author

Clark Kimberling, May 26 2011

Extensions

Name edited by Michel Marcus, Jul 29 2021

Status

approved