OFFSET
0,2
COMMENTS
Define sequences a(n) and b(n) recursively, starting with a(0) = 1, b(0) = 2:
b(n) = least new;
a(n) = a(n-1) + b(n) + b(n-1) + ... + b(0),
where "least new k" means the least positive integer not yet placed.
EXAMPLE
b(1) = least not in {a(0),b(0)} = 3;
a(1) = a(0) + b(1) + b(0) = 1 + 3 + 2 = 6.
MATHEMATICA
z = 1000;
mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
c = 1; a = {1}; b = {2}; x = {1};
Do[AppendTo[b, mex[Flatten[{a, b}], 1]];
AppendTo[x, 1];
AppendTo[a, c Last[a] + (Reverse[x] b // Total)], {z}]
Take[a, 30]
(* Peter J. C. Moses, May 10 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 12 2018
STATUS
approved