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A299420
Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 4, a(1) = 5; see Comments.
3
4, 5, 3, 8, 13, 16, 19, 21, 23, 26, 29, 32, 35, 38, 42, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 81, 84, 87, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 162, 165, 168, 171, 174
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
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] = 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
Sequence in context: A328238 A170929 A245085 * A374677 A019836 A353314
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 16 2018
STATUS
approved