login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A304807 Solution (a(n)) of the complementary equation a(n) = b(2n) + b(3n) ; see Comments. 3
2, 9, 14, 20, 27, 32, 39, 44, 51, 57, 62, 69, 75, 81, 87, 92, 99, 105, 111, 117, 122, 129, 134, 140, 147, 152, 159, 164, 170, 177, 182, 189, 194, 200, 207, 212, 219, 225, 231, 237, 242, 249, 255, 260, 267, 272, 279, 285, 290, 297, 302, 309, 314, 320, 327 (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(2n) + b(3n),

where "least new" means the least positive integer not yet placed.  Empirically, {a(n) - 6*n: n >= 0} = {2,3} and {5*b(n) - 6*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(2) + b(3), we must have a(1) >= 7, so that b(1) = 3, b(2) = 4, b(3) = 5, b(4) = 6, and a(1) = 9.

MATHEMATICA

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

h = 2; k = 3; 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]  (* A304807 *)

Take[b, 200]  (* A304808 *)

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

CROSSREFS

Cf. A304799, A304808.

Sequence in context: A226953 A274133 A288483 * A045920 A242466 A071344

Adjacent sequences:  A304804 A304805 A304806 * A304808 A304809 A304810

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 28 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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