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A297468 Solution (b(n)) of the system of 2 complementary equations in Comments. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 20 17:26 EDT 2021. Contains 345189 sequences. (Running on oeis4.)