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A304813 Solution (a(n)) of the complementary equation a(n) = b(3n) + b(5n); see Comments. 3
2, 12, 21, 29, 39, 48, 57, 66, 74, 84, 93, 101, 111, 120, 129, 138, 146, 156, 165, 173, 183, 191, 201, 210, 218, 228, 237, 245, 255, 263, 273, 282, 290, 300, 309, 317, 327, 335, 345, 354, 362, 372, 381, 390, 399, 407, 417, 426, 434, 444, 453, 462, 471, 479 (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(3n) + 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} = {7,8,9,10,11,12,13,14,15}.  See A304799 for a guide to related sequences.

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..9999

EXAMPLE

b(0) = 1, so that a(0) = 2.  Since a(1) = b(3) + b(5), we must have a(1) >= 10, so that b(1) = 3, b(2) = 4, b(3) = 5, b(4) = 6, b(5) = 7, and a(1) = 12.

MATHEMATICA

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

h = 3; 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]  (* A304813 *)

Take[b, 200]  (* A304814 *)

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

CROSSREFS

Cf. A304799, A304814.

Sequence in context: A048955 A034049 A271361 * A279424 A073041 A284595

Adjacent sequences:  A304810 A304811 A304812 * A304814 A304815 A304816

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 30 2018

STATUS

approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)