login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A299495 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 2, a(1) = 4, a(2) = 6; see Comments. 2
1, 3, 5, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 30, 31, 32, 34, 35, 37, 38, 40, 41, 42, 44, 45, 46, 48, 49, 50, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 70, 71, 72, 74, 75, 76, 78, 79, 80, 82, 83, 84, 86, 87, 88, 90 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

From the Bode-Harborth-Kimberling link:

a(n) = b(n-1) + b(n-2) + b(n-3) for n > 2;

b(0) = least positive integer not in {a(0),a(1),a(2)};

b(n) = least positive integer not in {a(0),...,a(n),b(0),...,b(n-1)} for n > 1.

Note that (b(n)) is strictly increasing and is the complement of (a(n)).

See A022424 for a guide to related sequences.

LINKS

Table of n, a(n) for n=0..65.

J-P. Bode, H. Harborth, C. Kimberling, Complementary Fibonacci sequences, Fibonacci Quarterly 45 (2007), 254-264.

MATHEMATICA

mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;

a[0] = 2; a[1] = 4; a[2] = 6; b[0] = 1; b[1] = 3; b[2] = 5;

a[n_] := a[n] = b[n - 1] + b[n - 2] + b[n - 3];

b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];

Table[a[n], {n, 0, 100}]    (* A299494 *)

Table[b[n], {n, 0, 100}]    (* A299495 *)

CROSSREFS

Cf. A022424, A299494.

Sequence in context: A188569 A274140 A212294 * A186689 A186350 A189829

Adjacent sequences:  A299492 A299493 A299494 * A299496 A299497 A299498

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 21 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 25 03:14 EDT 2019. Contains 323539 sequences. (Running on oeis4.)