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A304809
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Solution (a(n)) of the complementary equation a(n) = b(2n) + b(4n) ; see Comments.
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3
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2, 10, 17, 23, 31, 38, 44, 52, 59, 65, 73, 80, 86, 94, 101, 107, 115, 122, 128, 136, 143, 149, 157, 164, 170, 178, 185, 191, 199, 206, 212, 220, 227, 233, 241, 248, 254, 262, 269, 275, 283, 290, 296, 304, 311, 317, 325, 332, 338, 346, 353, 359, 367, 374, 380
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OFFSET
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0,1
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COMMENTS
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Define complementary sequences a(n) and b(n) recursively:
b(n) = least new,
a(n) = b(2n) + b(4n),
where "least new" means the least positive integer not yet placed. Empirically, {a(n) - 7*n: n >= 0} = {2,3} and {6*b(n) - 7*n: n >= 0} = {5,6,7,8,9,10,11}. See A304799 for a guide to related sequences.
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LINKS
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EXAMPLE
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b(0) = 1, so that a(0) = 2. Since a(1) = b(2) + b(4), we must have a(1) >= 8, so that b(1) = 3, b(2) = 4, b(3) = 5, b(4) = 6, b(5) = 7, and a(1) = 10.
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MATHEMATICA
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mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
h = 2; k = 4; a = {}; b = {1};
AppendTo[a, mex[Flatten[{a, b}], 1]];
Do[Do[AppendTo[b, mex[Flatten[{a, b}], Last[b]]], {k}];
AppendTo[a, Last[b] + b[[1 + (Length[b] - 1)/k h]]], {500}];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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