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A304809
Solution (a(n)) of the complementary equation a(n) = b(2n) + b(4n) ; see Comments.
3
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
OFFSET
0,1
COMMENTS
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.
LINKS
EXAMPLE
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.
MATHEMATICA
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}];
Take[a, 200] (* A304809 *)
Take[b, 200] (* A304810 *)
(* Peter J. C. Moses, May 14 2008 *)
CROSSREFS
Sequence in context: A009387 A305093 A316753 * A304805 A214086 A127492
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 28 2018
STATUS
approved