A191107 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-2 and 3x+1 are in a.

1, 4, 10, 13, 28, 31, 37, 40, 82, 85, 91, 94, 109, 112, 118, 121, 244, 247, 253, 256, 271, 274, 280, 283, 325, 328, 334, 337, 352, 355, 361, 364, 730, 733, 739, 742, 757, 760, 766, 769, 811, 814, 820, 823, 838, 841, 847, 850, 973, 976, 982, 985, 1000, 1003, 1009, 1012, 1054, 1057, 1063, 1066, 1081, 1084, 1090, 1093, 2188

Offset

1,2

Comments

For general discussions, see A190803 and A191106.

Numbers whose base-3 representation ends in 1 and contains no 2; primitive members of A005836. - Peter Munn, Aug 14 2023

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Barry Brent, On the Constant Terms of Certain Laurent Series, Preprints (2023) 2023061164.

Formula

Conjecture: a(n) = 3*A003278(n) - 2 = (A055246(n) + 1)/2. - L. Edson Jeffery, Nov 25 2015

Conjecture: a(n) = A190640(n)/2. - Michel Marcus, Aug 24 2016

Conjecture: a(n) = A003278(2n-1). - Arie Bos, Aug 07 2022

Maple

N:= 100000: # to get all terms <= N
with(queue):
Q:= new(1):
A:= {}:
while not empty(Q) do
  s:= dequeue(Q);
  A:= A union {s};
  for t in {3*s-2, 3*s+1} minus A do
    if t <= N then enqueue(Q, t) fi
  od
od:
sort(convert(A, list)); # Robert Israel, Nov 29 2015

Mathematica

h = 3; i = -2; j = 3; k = 1; f = 1;  g = 7;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191107 *)
b = (a + 2)/3; c = (a - 1)/3; r = Range[1, 900];
d = Intersection[b, r] (* A003278 *)
e = Intersection[c, r] (* A005836 *)

Crossrefs

Cf. A003278, A005836, A055246, A190640, A190803, A191106.

Sequence in context: A139121 A310359 A079932 * A173931 A173793 A076270

Adjacent sequences: A191104 A191105 A191106 * A191108 A191109 A191110

Keyword

nonn,base,easy

Author

Clark Kimberling, May 26 2011

Status

approved