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!)
A297469 Solution (bb(n)) of the system of 3 complementary equations in Comments. 9
2, 7, 11, 17, 22, 27, 31, 37, 41, 47, 51, 57, 62, 67, 71, 77, 82, 87, 91, 97, 102, 107, 111, 117, 121, 127, 131, 137, 142, 147, 151, 157, 161, 167, 171, 177, 182, 187, 191, 197, 201, 207, 211, 217, 222, 227, 231, 237, 242, 247, 251, 257, 262, 267, 271, 277 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Define sequences aa(n), bb(n), cc(n) recursively, starting with aa(0) = 1, bb(0) = 2, cc(0) = 3:

aa(n) = least new;

bb(n) = aa(n) + cc(n-1);

cc(n) = least new;

where "least new k" means the least positive integer not yet placed.

***

The sequences aa,bb,cc partition the positive integers. It appears that cc = A047218 and that for every n >=0,

(1) 5*n - 1 - 2*aa(n) is in {0,1,2},

(2) (aa(n) mod 5) is in {1,2,4},

(3) 5*n - 3 - bb(n) is in {0,1} for every n >= 0;

(4) (bb(n) mod 5) is in {1,2}.

From N. J. A. Sloane, Nov 05 2019 (Start)

Conjecture: For t >= 0, bb(2t) = 10t+1(+1 if binary expansion of t ends in an odd number of 0's), bb(2t+1) = 10t+7.

The first part may also be written as bb(2t) = 10t+1+A328789(t-1).

(End)

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..10000 [This is the sequence bb]

EXAMPLE

n:  0 1 2 3 4 5 6 7 8 9 10

aa: 1 4 6 9 12 14 16 19 21 24 26

bb: 2 7 11 17 22 27 31 37 41 47 51

cc: 3 5 8 10 13 15 18 20 23 25 28

MATHEMATICA

z = 500;

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

a = {1}; b = {2}; c = {3};

Do[AppendTo[a, mex[Flatten[{a, b, c}], Last[a]]];

  AppendTo[b, Last[a] + Last[c]];

  AppendTo[c, mex[Flatten[{a, b, c}], Last[a]]], {z}];

Take[a, 100] (* A298468 *)

Take[b, 100] (* A297469 *)

Take[c, 100] (* A047218 *)

(* Peter J. C. Moses, Apr 23 2018 *)

CROSSREFS

Cf. A299634, A298468 (aa), A047218 (cc), A328789.

Sequence in context: A063205 A090613 A063097 * A168421 A038942 A175283

Adjacent sequences:  A297466 A297467 A297468 * A297470 A297471 A297472

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 04 2018

EXTENSIONS

Changed a,b,c to aa,bb,cc to avoid confusion caused by conflict with standard OEIS terminology. - N. J. A. Sloane, Nov 03 2019

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 April 6 18:51 EDT 2020. Contains 333286 sequences. (Running on oeis4.)