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!)
A299544 Solution b( ) of the complementary equation a(n) = 2*b(n-1) + b(n-2) - b(n-3), where a(0) = 1, a(1) = 2, a(2) = 3; see Comments. 3
4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 24, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 58, 59, 60, 62, 63, 66, 68, 69, 70, 72, 73, 76, 77, 78, 80, 81, 84, 85, 86, 88, 89, 92, 93, 94, 96, 97, 100, 101 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From the Bode-Harborth-Kimberling link:

a(n) = 2*b(n-1) + b(n-2) - 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] = 2 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}]    (* A299543 *)

Table[b[n], {n, 0, 100}]    (* A299544 *)

CROSSREFS

Cf. A022424, A299543.

Sequence in context: A111222 A037357 A191842 * A039174 A016069 A194283

Adjacent sequences:  A299541 A299542 A299543 * A299545 A299546 A299547

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 25 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.)