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A304803 Solution (a(n)) of the complementary equation a(n) = b(n) + b(4n); see Comments. 3
2, 9, 15, 21, 26, 32, 38, 45, 51, 56, 62, 68, 75, 81, 87, 92, 98, 105, 111, 117, 122, 129, 135, 141, 146, 152, 159, 165, 171, 176, 182, 189, 195, 201, 206, 212, 218, 225, 231, 236, 242, 248, 255, 261, 267, 272, 279, 285, 291, 297, 302, 309, 315, 321, 326 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Define complementary sequences a(n) and b(n) recursively:

b(n) = least new,

a(n) = b(n) + b(4n),

where "least new" means the least positive integer not yet placed.  Empirically, {a(n) - 5*n: n >= 0} = {2,3} and {4*b(n) - 5*n: n >= 0} = {4,5,6,7,8,9}.  See A304799 for a guide to related sequences.

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(4), we must have a(1) >= 9, so that b(1) = 3, b(2) = 4, b(3) = 5, b(4) = 6, b(5) = 7, b(6) = 8, and a(1) = 9.

MATHEMATICA

mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);

h = 1; 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]  (* A304803 *)

Take[b, 200]  (* A304804 *)

(* Peter J. C. Moses, May 14 2008 *)

CROSSREFS

Cf. A304799, A304804.

Sequence in context: A057481 A083288 A272044 * A184531 A063105 A215035

Adjacent sequences:  A304800 A304801 A304802 * A304804 A304805 A304806

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 19 2018

STATUS

approved

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Last modified May 12 06:54 EDT 2021. Contains 343820 sequences. (Running on oeis4.)