A297467 Solution (a(n)) of the system of 2 complementary equations in Comments.

1, 2, 10, 31, 35, 95, 99, 108, 112, 289, 293, 302, 306, 330, 335, 343, 348, 875, 880, 888, 893, 916, 921, 929, 934, 1002, 1007, 1018, 1023, 1043, 1048, 1059, 1064, 2641, 2646, 2657, 2662, 2682, 2687, 2698, 2703, 2768, 2773, 2784, 2789, 2809, 2814, 2825, 2830

Offset

0,2

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..2000

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, A297468.

Sequence in context: A268688 A281069 A156492 * A305011 A090809 A051747

Adjacent sequences: A297464 A297465 A297466 * A297468 A297469 A297470

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2018

Status

approved