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A297149 Solution (c(n)) of the system of 3 complementary equations in Comments. 3
4, 11, 26, 46, 69, 95, 124, 158, 196, 239, 286, 336, 389, 445, 504, 566, 631, 699, 770, 844, 923, 1006, 1092, 1181, 1273, 1370, 1471, 1575, 1682, 1792, 1905, 2021, 2140, 2262, 2387, 2515, 2646, 2780, 2919, 3062, 3208, 3357, 3509, 3664, 3824, 3988, 4155, 4325 (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, A296502.

Sequence in context: A079467 A140897 A008263 * A159944 A002763 A077270

Adjacent sequences:  A297146 A297147 A297148 * A297150 A297151 A297152

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 24 2018

STATUS

approved

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Last modified July 5 15:26 EDT 2020. Contains 335473 sequences. (Running on oeis4.)