A297468 - OEIS

%I #4 Apr 25 2018 08:33:11

%S 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,

%T 29,30,32,33,34,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,

%U 54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71

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

%C Define sequences a(n), b(n), c(n) recursively, starting with a(0) = 1, a(1) = 1, b(0) = 3; for n >= 1,

%C a(2n) = 3*a(n) + b(n);

%C a(2n+1) = 3*a(n-1) + n;

%C b(n) = least new;

%C where "least new k" means the least positive integer not yet placed.  The sequences (a(n)) and (b(n)) are complementary.

%H Clark Kimberling, <a href="/A297468/b297468.txt">Table of n, a(n) for n = 0..1000</a>

%e n:   0  1   2   3   4   5   6   7   8

%e a:   1  2  10  31  35  95  99 108 112

%e b:   3  4   5   6   7   8   9  11  12

%t z = 300;

%t mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);

%t a = {1, 2}; b = {3};

%t Do[AppendTo[b, mex[Flatten[{a, b}], Last[b]]];

%t  AppendTo[a, 3 a[[#/2 + 1]] + b[[#/2 + 1]]] &[Length[a]];

%t  AppendTo[a, 3 a[[(# + 3)/2]] + (# - 1)/2] &[Length[a]], {z}]

%t Take[a, 100]  (* A297467 *)

%t Take[b, 100]  (* A297468 *)

%t (* _Peter J. C. Moses_,  Apr 22 2018 *)

%Y Cf. A299634, A297467.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Apr 24 2018