A297467 -id:A297467 - cp's OEIS frontend

A297468 Solution (b(n)) of the system of 2 complementary equations in Comments.

3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71

Offset: 0

Clark Kimberling, Apr 24 2018

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.

			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

Clark Kimberling, Table of n, a(n) for n = 0..1000

Cf. A299634, A297467.

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 *)

cp's OEIS Frontend

A297468 Solution (b(n)) of the system of 2 complementary equations in Comments.

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