



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
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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(n1), v(1), ..., v(n1)} and v(n) = n  1 + k + least positive integer not in {u(1), ..., u(n1), u(n), v(1), ..., v(n1)}. 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.
Sequence in context: A285915 A075329 A177031 * A159018 A345980 A005427
Adjacent sequences: A336005 A336006 A336007 * A336009 A336010 A336011


KEYWORD

nonn


AUTHOR

Clark Kimberling, Jul 16 2020


EXTENSIONS

Corrected by Clark Kimberling, Sep 26 2020


STATUS

approved



