

A304800


Solution (b(n)) of the complementary equation a(n) = b(n) + b(2n); see Comments.


3



1, 3, 4, 5, 6, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 22, 24, 25, 27, 28, 29, 30, 32, 33, 35, 36, 37, 39, 40, 41, 42, 44, 45, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 60, 61, 63, 64, 65, 67, 68, 69, 70, 72, 73, 75, 76, 77, 78, 80, 81, 83, 84, 85, 87, 88
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OFFSET

0,2


COMMENTS

Define complementary sequences a(n) and b(n) recursively:
b(n) = least new,
a(n) = b(n) + b(2n),
where "least new" means the least positive integer not yet placed. See A304799 for a guide to related sequences. Empirically, {a(n)  3*n: n >= 0} = {2,3} and {2*b(n)  3*n : n >= 0} = {2,3,4,5}.


LINKS

Clark Kimberling, Table of n, a(n) for n = 0..10000


EXAMPLE

b(0) = 1, so that a(0) = 2. Since a(1) = b(1) + b(2), we must have a(1) >= 7, so that b(1) = 3, b(2) = 4, b(3) = 5, b(4) = 6, and a(1) = 7.


MATHEMATICA

mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
h = 1; k = 2; 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] (* A304799 *)
Take[b, 200] (* A304800 *)
(* Peter J. C. Moses, May 14 2008 *)


CROSSREFS

Cf. A304799.
Sequence in context: A047428 A218784 A039066 * A197911 A298007 A026363
Adjacent sequences: A304797 A304798 A304799 * A304801 A304802 A304803


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, May 19 2018


STATUS

approved



