A298876 Solution (c(n)) of the system of 3 equations in Comments.

3, 16, 27, 43, 60, 79, 100, 126, 153, 182, 213, 249, 289, 330, 373, 418, 465, 514, 565, 624, 683, 744, 807, 872, 939, 1008, 1082, 1157, 1234, 1313, 1394, 1477, 1562, 1652, 1746, 1841, 1938, 2037, 2138, 2241, 2346, 2453, 2562, 2673, 2786, 2904, 3023, 3147

Offset

0,1

Comments

Define sequences a(n), b(n), c(n) recursively, starting with a(0) = 1, b(0) = 2:

a(n) = least new;

b(n) = a(n) + b(n-1);

c(n) = a(n) + 2 b(n);

where "least new k" means the least positive integer not yet placed.

***

Do these sequences a,b,c partition the positive integers? They differ from the corresponding partitioning sequences A298871, A298872, and A298872. For example, A298872(56) = 2139, whereas A298875(56) = 2138.

Differs from A298873 first at n=56. - Georg Fischer, Oct 10 2018

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Example

n:   0    1    2    3    4    5    6    7    8    9
a:   1    4    5    7    8    9   10   12   13   14
b:   2    6   11   18   26   35   45   57   70   84
c:   3   16   27   43   60   30   79  100  126  153

Mathematica

z = 200;
mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
a = {1}; b = {2}; c = {3};
Do[{AppendTo[a, mex[Flatten[{a, b, c}], 1]],
   AppendTo[b, Last[a] + Last[b]],
   AppendTo[c, Last[a] + 2 Last[b]]}, {z}];
Take[a, 100]  (* A298874 *)
Take[b, 100]  (* A298875 *)
Take[c, 100]  (* A298876 *)

Crossrefs

Cf. A299634, A298871, A298874, A298875.

Sequence in context: A193367 A322413 A298873 * A258717 A013196 A371382

Adjacent sequences: A298873 A298874 A298875 * A298877 A298878 A298879

Keyword

nonn,easy

Author

Clark Kimberling, Apr 19 2018

Status

approved