A336008 - OEIS

%I #25 Sep 26 2020 11:48:39

%S 5,7,9,12,15,18,20,23,25,28,30,33,36,38,41,44,46,49,52,54,57,59,62,65,

%T 67,70,72,75,78,80,83,85,88,91,93,96,99,101,104,106,109,112,114,117,

%U 120,122,125,127,130,133,135,138,141,143,146,148,151,154,156,159

%N Complement of A335999.

%C 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.

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

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

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

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

%t a  (* A335999 *)

%t b  (* A336008 *)

%t (* _Peter J. C. Moses_, Jul 13 2020 *)

%Y Cf. A335999.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jul 16 2020

%E Corrected by _Clark Kimberling_, Sep 26 2020