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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A299547 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2) + ... + b(0), where a(0) = 1, a(1) = 2, a(2) = 3; see Comments. 2
1, 2, 3, 12, 18, 25, 33, 42, 52, 63, 76, 90, 105, 121, 138, 157, 177, 198, 220, 243, 267, 293, 320, 348, 377, 407, 438, 470, 504, 539, 575, 612, 650, 689, 729, 770, 813, 857, 902, 948, 995, 1043, 1092, 1142, 1193, 1246, 1300, 1355, 1411, 1468, 1526, 1585 (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(0) 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..51.

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;

a[n_] := a[n] = Sum[b[k], {k, 0, n - 1}];

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

Table[a[n], {n, 0, 100}]    (* A299547 *)

CROSSREFS

Cf. A022424.

Sequence in context: A112976 A100570 A056700 * A140989 A281086 A130089

Adjacent sequences:  A299544 A299545 A299546 * A299548 A299549 A299550

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 March 24 19:42 EDT 2019. Contains 321448 sequences. (Running on oeis4.)