

A299421


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


3



1, 2, 6, 7, 9, 10, 11, 12, 14, 15, 17, 18, 20, 22, 24, 25, 27, 28, 30, 31, 33, 34, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 80, 82, 83, 85, 86, 88, 90, 91, 93, 94, 96, 97, 99, 100
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OFFSET

0,2


COMMENTS

a(n) = b(n1) + b(n2) 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(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..2000
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] = 4; a[1] = 5; b[0] = 1; b[1] = 2;
a[n_] := a[n] = b[n  1] + b[n  2];
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n  1}]]];
Table[a[n], {n, 0, 100}] (* A299420 *)
Table[b[n], {n, 0, 100}] (* A299421 *)


CROSSREFS

Cf. A022424, A299420.
Sequence in context: A296443 A102046 A019913 * A327181 A047554 A206446
Adjacent sequences: A299418 A299419 A299420 * A299422 A299423 A299424


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Feb 16 2018


STATUS

approved



