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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.
10
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
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
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, May 26 2011
STATUS
approved