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!)
A304815 Solution (a(n)) of the complementary equation a(n) = b(4n) + b(5n); see Comments. 3
2, 13, 22, 33, 43, 53, 63, 72, 83, 92, 103, 112, 123, 133, 143, 153, 163, 173, 182, 193, 203, 213, 223, 233, 243, 253, 263, 272, 283, 292, 303, 313, 323, 333, 342, 353, 362, 373, 382, 393, 403, 413, 423, 432, 443, 452, 463, 472, 483, 493, 503, 513, 522, 533 (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(4n) + b(5n),

where "least new" means the least positive integer not yet placed.  Empirically, {a(n) - 8*n: n >= 0} = {2,3} and {7*b(n) - 8*n: n >= 0} = {8,9,10,11,12,13,14,15,16,17}.  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(4) + b(5), we must have a(1) >= 11, so that b(1) = 3, b(2) = 4, b(3) = 5, b(4) = 6, b(5) = 7, and a(1) = 13.

MATHEMATICA

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

h = 4; k = 5; 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]  (* A304815 *)

Take[b, 200]  (* A304816 *)

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

CROSSREFS

Cf. A304799, A304816.

Sequence in context: A085509 A127485 A061385 * A156179 A090519 A018540

Adjacent sequences:  A304812 A304813 A304814 * A304816 A304817 A304818

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 30 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 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)