A336008 - OEIS

A336008

Complement of A335999.

5, 7, 9, 12, 15, 18, 20, 23, 25, 28, 30, 33, 36, 38, 41, 44, 46, 49, 52, 54, 57, 59, 62, 65, 67, 70, 72, 75, 78, 80, 83, 85, 88, 91, 93, 96, 99, 101, 104, 106, 109, 112, 114, 117, 120, 122, 125, 127, 130, 133, 135, 138, 141, 143, 146, 148, 151, 154, 156, 159

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

In general, let u(1) = 1, and let k be a positive integer. Define u(n) = least positive integer not in {u(1), ..., u(n-1), v(1), ..., v(n-1)} and v(n) = n - 1 + k + least positive integer not in {u(1), ..., u(n-1), u(n), v(1), ..., v(n-1)}. As sets, (u(n)) and (v(n)) are disjoint. If k >=-1, let a(n) = u(n) and b(n) = v(n) for all n >= 1, but if k <= -2, let a(n) = u(n) - k + 1 and b(n) = v(n) - k -1 for all n >= 1. Then every positive integer is in exactly one of the sequences (a(n)) and b(n)). The difference sequence of (a(n)) consists of 1's and 2's; the difference sequence of (b(n)) consists of 2's and 3's. See A335999 for a guide to related sequences.

LINKS

Table of n, a(n) for n=1..60.

MATHEMATICA

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

{a, b} = {{1}, {}}; k = 3;

Do[AppendTo[b, Length[b] + k + mex[Flatten[{a, b}], Last[a]]];

AppendTo[a, mex[Flatten[{a, b}], Last[a]]], {150}]

a (* A335999 *)

b (* A336008 *)

(* Peter J. C. Moses, Jul 13 2020 *)

CROSSREFS

Cf. A335999.