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A299418 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 3, a(1) = 5; see Comments. 3
3, 5, 3, 6, 11, 15, 17, 19, 22, 25, 27, 30, 34, 38, 41, 44, 47, 50, 54, 57, 60, 63, 65, 68, 71, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 105, 108, 111, 114, 117, 120, 123, 126, 130, 133, 136, 139, 142, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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)).

See A022424 for a guide to related sequences.

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..2000

J-P. Bode, H. Harborth, C. Kimberling, Complementary Fibonacci sequences, Fibonacci Quarterly 45 (2007), 254-264.

MATHEMATICA

mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;

a[0] = 3; 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}]  (* A299418 *)

Table[b[n], {n, 0, 100}]  (* A299419 *)

CROSSREFS

Cf. A022424, A299419.

Sequence in context: A100667 A286108 A096438 * A214456 A118271 A260689

Adjacent sequences:  A299415 A299416 A299417 * A299419 A299420 A299421

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 15 2018

STATUS

approved

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Last modified June 15 16:13 EDT 2019. Contains 324142 sequences. (Running on oeis4.)