OFFSET
0,1
COMMENTS
Define sequences a(n), b(n), c(n) recursively, starting with a(0) = 1, a(1) = 1, b(0) = 3; for n >= 1,
a(2n) = 3*a(n) + b(n);
a(2n+1) = 3*a(n-1) + n;
b(n) = least new;
where "least new k" means the least positive integer not yet placed. The sequences (a(n)) and (b(n)) are complementary.
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..1000
EXAMPLE
n: 0 1 2 3 4 5 6 7 8
a: 1 2 10 31 35 95 99 108 112
b: 3 4 5 6 7 8 9 11 12
MATHEMATICA
z = 300;
mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
a = {1, 2}; b = {3};
Do[AppendTo[b, mex[Flatten[{a, b}], Last[b]]];
AppendTo[a, 3 a[[#/2 + 1]] + b[[#/2 + 1]]] &[Length[a]];
AppendTo[a, 3 a[[(# + 3)/2]] + (# - 1)/2] &[Length[a]], {z}]
Take[a, 100] (* A297467 *)
Take[b, 100] (* A297468 *)
(* Peter J. C. Moses, Apr 22 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 24 2018
STATUS
approved