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!)
A299536 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-3), where a(0) = 1, a(1) = 2, a(2) = 3; see Comments. 3
4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 18, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 34, 35, 36, 38, 40, 41, 42, 44, 46, 47, 49, 50, 52, 54, 55, 57, 58, 60, 62, 63, 64, 66, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 94, 96, 98, 99, 100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From the Bode-Harborth-Kimberling link:

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

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

a[n_] := a[n] = b[n - 1] + 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}]    (* A022427 *)

Table[b[n], {n, 0, 100}]    (* A299536 *)

CROSSREFS

Cf. A022424, A022427 (complement).

Sequence in context: A173888 A120181 A016070 * A321025 A047569 A039062

Adjacent sequences:  A299533 A299534 A299535 * A299537 A299538 A299539

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 24 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 September 20 10:24 EDT 2020. Contains 337264 sequences. (Running on oeis4.)