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

0,1

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

Cf. A299634, A297467.

Sequence in context: A137913 A137937 A260580 * A047565 A026466 A304806

Adjacent sequences: A297465 A297466 A297467 * A297469 A297470 A297471

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2018

Status

approved