The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A022424 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 1, a(1) = 2; see Comments. 58
 1, 2, 7, 9, 11, 14, 18, 22, 25, 28, 31, 33, 36, 39, 41, 44, 47, 50, 53, 56, 59, 62, 66, 69, 72, 75, 78, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 161, 164, 167, 170 (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) for n > 2; b(0) = least positive integer not in {a(0),a(1)}; 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)). *** In the following guide to solutions a( ) and b( ) of a(n) = b(n-1) + b(n-2), an asterisk (*) indicates that a( ) differs from the indicated A-sequence in one or two initial terms: (a(n))     (b(n))    a(0)   a(1) A022424    A055563     1      2 A022425    A299407     1      4 A022441*   A055562     1      5 A022426    A299411     2      3 A022442*   A099467*    2      4 A299416    A299417     3      4 A299418    A299419     3      5 A299420    A299421     4      5 A022441*   A055562     1      1 *** Guide to solutions a( ) and b( ) of a(n) = b(n-1) + b(n-2) + b(n-3) for various initial values: (a(n))     (b(n))    a(0)   a(1)   a(2) A299486    A299487     1      2      3 A299488    A299489     1      2      4 A299490    A299491     1      3      5 A299492    A299492     2      4      5 A299494    A299493     2      4      6 A299496    A299494     3      4      5 *** Guide to other complementary equations: A022427-A022440:  a(n) = b(n-1) + b(n-3) A299531-A299532:  a(n) = 2*b(n-1) + b(n-2), a(0) = 1, a(1) = 2 A296220, A299534: a(n) = b(n-1) + 2*b(n-2), a(0) = 1, a(1) = 2 A022437, A299536: a(n) = b(n-1) + b(n-3), a(0) = 1, a(1) = 2, a(2) = 3 A022437, A299538: a(n) = b(n-1) + b(n-3), a(0) = 2, a(1) = 3, a(2) = 4 A022438-A299540:  a(n) = b(n-1) + b(n-3), a(0) = 2, a(1) = 3, a(2) = 5 A299541-A299542:  a(n) = b(n-1) + b(n-3), a(0) = 2, a(1) = 4, a(2) = 6 A299543-A299544:  a(n) = 2*b(n-1) + b(n-2) - b(n-3), a(0) = 1, a(1) = 2, a(2) = 3 A299545-A299546:  a(n) = b(n-1) + 2*b(n-2) - b(n-3), a(0) = 1, a(1) = 2, a(2) = 3 A299547: a(n) = b(n-1) + b(n-2) + ... + b(0), a(0) = 1, a(1) = 2, a(2) = 3 LINKS Ivan Neretin, Table of n, a(n) for n = 0..10000 J-P. Bode, H. Harborth, C. Kimberling, Complementary Fibonacci sequences, Fibonacci Quarterly 45 (2007), 254-264. MATHEMATICA Fold[Append[#1, Plus @@ Complement[Range[Max@#1 + 3], #1][[{#2, #2 + 1}]]] &, {1, 2}, Range[56]] (* Ivan Neretin, Mar 28 2017 *) CROSSREFS Cf. A055563 (complement), A022425, A299407, A299486-A299494. Another pair is given in A324142, A324143. Sequence in context: A003668 A191263 A287359 * A136498 A297826 A288598 Adjacent sequences:  A022421 A022422 A022423 * A022425 A022426 A022427 KEYWORD nonn AUTHOR EXTENSIONS Edited by Clark Kimberling, Feb 16 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.

Last modified August 11 04:02 EDT 2020. Contains 336421 sequences. (Running on oeis4.)