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!)
A299545 Solution a( ) of the complementary equation a(n) = b(n-1) + 2*b(n-2) - b(n-3), where a(0) = 1, a(1) = 2, a(2) = 3; see Comments. 3
1, 2, 3, 12, 14, 16, 18, 20, 22, 25, 30, 34, 38, 42, 46, 49, 51, 55, 56, 58, 61, 65, 66, 69, 73, 74, 77, 81, 82, 85, 89, 90, 93, 97, 99, 104, 107, 108, 112, 119, 121, 123, 127, 128, 132, 138, 139, 143, 144, 148, 154, 155, 159, 160, 164, 170, 171, 175, 176 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

From the Bode-Harborth-Kimberling link:

a(n) = b(n-1) + 2*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..58.

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] + 2 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}]    (* A299545 *)

Table[b[n], {n, 0, 100}]    (* A299546 *)

CROSSREFS

Cf. A022424, A299546.

Sequence in context: A039588 A024579 A291565 * A068603 A045878 A295398

Adjacent sequences:  A299542 A299543 A299544 * A299546 A299547 A299548

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 01 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 10:49 EDT 2020. Contains 337264 sequences. (Running on oeis4.)