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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
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 24 2018
STATUS
approved