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A296502 Solution (b(n)) of the system of 3 complementary equations in Comments. 3
2, 5, 14, 32, 53, 77, 104, 134, 170, 209, 254, 302, 353, 407, 464, 524, 587, 653, 722, 794, 869, 950, 1034, 1121, 1211, 1304, 1403, 1505, 1610, 1718, 1829, 1943, 2060, 2180, 2303, 2429, 2558, 2690, 2825, 2966, 3110, 3257, 3407, 3560, 3716, 3878, 4043, 4211 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Define sequences a(n), b(n), c(n) recursively, starting with a(0) = 1, b(0) = 2, c(0) = 4:

a(n) = least new;

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

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

where "least new k" means the least positive integer not yet placed. The sequences a,b,c partition the positive integers.

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   3    6    7    8    9   10   12  13    15

b:   2   5   14   32   53   77  104  134  170  209

c:   4  11   26   46   69   95  124  158  196  239

MATHEMATICA

z = 300;

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

a = {1}; b = {2}; c = {4}; n = 1;

Do[{n++, AppendTo[a, mex[Flatten[{a, b, c}], 1]],

   AppendTo[b, a[[n - 1]] + c[[n - 1]]],

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

Take[a, 100]  (* A296484 *)

Take[b, 100]  (* A296502 *)

Take[c, 100]  (* A297149 *)

CROSSREFS

Cf. A299634, A296484, A297149.

Sequence in context: A212393 A056358 A336229 * A036681 A125615 A096772

Adjacent sequences:  A296499 A296500 A296501 * A296503 A296504 A296505

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 24 2018

STATUS

approved

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Last modified October 24 01:18 EDT 2021. Contains 348217 sequences. (Running on oeis4.)