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A294861 Solution of the complementary equation a(n) = a(n-2) + b(n-2) + 1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences. 2
1, 2, 5, 7, 12, 16, 22, 27, 34, 41, 49, 57, 67, 76, 87, 97, 109, 121, 134, 147, 161, 176, 191, 207, 223, 240, 257, 276, 294, 314, 333, 354, 374, 397, 418, 442, 464, 489, 512, 538, 563, 590, 616, 644, 671, 700, 728, 759, 788, 820, 850, 883, 914, 948, 980 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A294860 for a guide to related sequences.
LINKS
Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13.
EXAMPLE
a(0) = 1, a(1) = 2, b(0) = 3
b(1) = 4 (least "new number")
a(2) = a(0) + b(0) + 1 = 5
Complement: (b(n)) = (3, 4, 6, 8, 9, 10, 11, 12, 14, 15, 17, ...)
MATHEMATICA
mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 2; b[0] = 3;
a[n_] := a[n] = a[n - 2] + b[n - 2] + 1;
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
Table[a[n], {n, 0, 18}] (* A294861 *)
Table[b[n], {n, 0, 10}]
CROSSREFS
Sequence in context: A024702 A343944 A226084 * A161664 A080547 A080555
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Nov 16 2017
STATUS
approved

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Last modified April 17 04:42 EDT 2024. Contains 371756 sequences. (Running on oeis4.)