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A297293 Solution (c(n)) of the system of 3 complementary equations in Comments. 3
2, 8, 10, 18, 24, 26, 33, 35, 42, 45, 54, 56, 63, 66, 74, 76, 82, 88, 94, 96, 102, 105, 114, 116, 123, 125, 134, 136, 142, 145, 154, 156, 162, 168, 170, 178, 180, 186, 194, 196, 202, 208, 214, 216, 222, 225, 234, 236, 243, 246, 254, 256, 262, 265, 274, 276 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Define sequences a(n), b(n), c(n) recursively:

a(n) = least new;

b(n) = least new > = a(n) + 2;

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

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

***

The sequences a,b,c partition the positive integers.

***

Conjectures:  for n >= 0,

0 <= 5*n + 4 - 2*a(n) <= 5,

0 <= 5*n + 8 - 2*b(n) <= 4,

0 <= c(n) - 5n <= 4.

LINKS

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

EXAMPLE

n:   0   1   2   3   4   5   6   7   8   9  10

a:   1   4   5   9  12  13  16  17  21  27  28

b:   3   6   7  11  14  15  19  20  23  25  29

c:   2   8  10  18  24  26  33  35  42  45  54

MATHEMATICA

z = 300;

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

a = b = c = {};

Do[{AppendTo[a,

    mex[Flatten[{a, b, c}], If[Length[a] == 0, 1, Last[a]]]],

   AppendTo[b, mex[Flatten[{a, b, c}], Last[a] + 2]],

   AppendTo[c, Last[a] + Last[b] - 2]}, {z}];

Take[a, 100]  (* A297291 *)

Take[b, 100]  (* A297292 *)

Take[c, 100]  (* A297293 *)

(* Peter J. C. Moses, Apr 23 2018 *)

CROSSREFS

Cf. A299634, A297291, A297292.

Sequence in context: A197115 A288824 A190042 * A294157 A082396 A195582

Adjacent sequences:  A297290 A297291 A297292 * A297294 A297295 A297296

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 24 2018

STATUS

approved

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Last modified February 16 21:12 EST 2019. Contains 320199 sequences. (Running on oeis4.)