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A298874 Solution (a(n)) of the system of 3 equations in Comments. 5
1, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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.
LINKS
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
Sequence in context: A182757 A164515 A298871 * A266267 A189477 A047494
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 19 2018
STATUS
approved

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)