

A299487


Solution b( ) of the complementary equation a(n) = b(n1) + b(n2) + b(n3), where a(0) = 1, a(1) = 2, a(2) = 3; see Comments.


3



4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 89
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

a(n) = b(n1) + b(n2) + b(n3) for n > 2;
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(n1)} 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

Clark Kimberling, Table of n, a(n) for n = 0..1000
JP. Bode, H. Harborth, C. Kimberling, Complementary Fibonacci sequences, Fibonacci Quarterly 45 (2007), 254264.


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; b[2] = 6;
a[n_] := a[n] = 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}]]];
u = Table[a[n], {n, 0, 100}] (* A299486 *)
v = Table[b[n], {n, 0, 100}] (* A299487 *)


CROSSREFS

Cf. A022424, A299486.
Sequence in context: A026456 A026425 A026440 * A063713 A026462 A039230
Adjacent sequences: A299484 A299485 A299486 * A299488 A299489 A299490


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Feb 16 2018


STATUS

approved



