

A299540


Solution b( ) of the complementary equation a(n) = b(n1) + b(n3), where a(0) = 2, a(1) = 3, a(2) = 5; see Comments.


3



1, 4, 6, 8, 9, 10, 11, 13, 14, 16, 17, 19, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 72, 73, 74, 76, 78, 79, 80, 82, 84, 85, 87, 88, 90, 92, 93, 94, 96, 98, 99, 100
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OFFSET

0,2


COMMENTS

From the BodeHarborthKimberling link:
a(n) = b(n1) + b(n3) 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(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

Table of n, a(n) for n=0..65.
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] = 2; a[1] = 3; a[2] = 5; b[0] = 1; b[1] = 4;
a[n_] := a[n] = b[n  1] + 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}] (* A022438 *)
Table[b[n], {n, 0, 100}] (* A299540 *)


CROSSREFS

Cf. A022424, A022438.
Sequence in context: A045762 A320985 A047748 * A085558 A084984 A104499
Adjacent sequences: A299537 A299538 A299539 * A299541 A299542 A299543


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Feb 25 2018


STATUS

approved



