

A299493


Solution b( ) of the complementary equation a(n) = b(n1) + b(n2) + b(n3), where a(0) = 1, a(1) = 4, a(2) = 5; see Comments.


3



1, 3, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 25, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 58, 59, 60, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89
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OFFSET

0,2


COMMENTS

From the BodeHarborthKimberling link:
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

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] = 4; a[2] = 5; b[0] = 1; b[1] = 3; 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}]]];
Table[a[n], {n, 0, 100}] (* A299492 *)
Table[b[n], {n, 0, 100}] (* A299493 *)


CROSSREFS

Cf. A022424, A299492.
Sequence in context: A048748 A030781 A073417 * A047559 A288742 A113826
Adjacent sequences: A299490 A299491 A299492 * A299494 A299495 A299496


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Feb 20 2018


STATUS

approved



