cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A299489 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 1, a(1) = 2, a(2) = 4; see Comments.

Original entry on oeis.org

3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 89
Offset: 0

Views

Author

Clark Kimberling, Feb 16 2018

Keywords

Comments

a(n) = b(n-1) + b(n-2) + b(n-3) 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(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

Crossrefs

Cf. A022424, A299488.

Programs

  • Mathematica
    mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 2; a[2] = 4; b[0] = 3; b[1] = 5; 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}]    (* A299488 *)
Table[b[n], {n, 0, 100}]    (* A299489 *)

A299490 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 1, a(1) = 3, a(2) = 5; see Comments.

Original entry on oeis.org

1, 3, 5, 12, 17, 21, 24, 27, 30, 34, 38, 42, 45, 49, 53, 57, 61, 65, 70, 74, 79, 83, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 204, 208, 212, 216, 220, 224
Offset: 0

Views

Author

Clark Kimberling, Feb 16 2018

Keywords

Comments

a(n) = b(n-1) + b(n-2) + b(n-3) 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(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

Crossrefs

Cf. A022424, A299491.

Programs

  • Mathematica
    mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 3; a[2] = 5; b[0] = 2; b[1] = 4; 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}]    (* A299490 *)
Table[b[n], {n, 0, 100}]    (* A299491 *)

A299491 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 1, a(1) = 3, a(2) = 5; see Comments.

Original entry on oeis.org

2, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 46, 47, 48, 50, 51, 52, 54, 55, 56, 58, 59, 60, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 89
Offset: 0

Views

Author

Clark Kimberling, Feb 16 2018

Keywords

Comments

a(n) = b(n-1) + b(n-2) + b(n-3) 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(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

Crossrefs

Cf. A022424, A299490.

Programs

  • Mathematica
    mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 3; a[2] = 5; b[0] = 2; b[1] = 4; 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}]]];
u = Table[a[n], {n, 0, 100}]    (* A299490 *)
v = Table[b[n], {n, 0, 100}]    (* A299491 *)

A299492 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 2, a(1) = 4, a(2) = 5; see Comments.

Original entry on oeis.org

2, 4, 5, 10, 16, 21, 24, 28, 32, 36, 39, 42, 46, 50, 54, 57, 61, 65, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 115, 119, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 169, 173, 177, 181, 185, 189, 193, 197, 201, 204, 208, 212, 216, 220, 224
Offset: 0

Views

Author

Clark Kimberling, Feb 20 2018

Keywords

Comments

From the Bode-Harborth-Kimberling link:
a(n) = b(n-1) + b(n-2) + b(n-3) 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(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

Crossrefs

Cf. A022424, A299493.

Programs

  • 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 *)

A299493 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 2, a(1) = 4, a(2) = 5; see Comments.

Original entry on oeis.org

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
Offset: 0

Views

Author

Clark Kimberling, Feb 20 2018

Keywords

Comments

From the Bode-Harborth-Kimberling link:
a(n) = b(n-1) + b(n-2) + b(n-3) 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(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

Crossrefs

Cf. A022424, A299492.

Programs

  • 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 *)

Extensions

Definition corrected by Georg Fischer, Sep 28 2020

A299494 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 2, a(1) = 4, a(2) = 6; see Comments.

Original entry on oeis.org

2, 4, 6, 9, 15, 20, 25, 29, 33, 36, 39, 43, 47, 51, 54, 58, 62, 66, 69, 73, 77, 81, 85, 89, 93, 97, 101, 106, 110, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 205, 209, 213, 217, 221, 225, 229
Offset: 0

Views

Author

Clark Kimberling, Feb 21 2018

Keywords

Comments

From the Bode-Harborth-Kimberling link:
a(n) = b(n-1) + b(n-2) + b(n-3) 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(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

Crossrefs

Cf. A022424, A299495.

Programs

  • Mathematica
    mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 2; a[1] = 4; a[2] = 6; b[0] = 1; b[1] = 3; b[2] = 5;
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}]    (* A299494 *)
Table[b[n], {n, 0, 100}]    (* A299495 *)

A299496 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 3, a(1) = 4, a(2) = 5; see Comments.

Original entry on oeis.org

3, 4, 5, 6, 12, 18, 24, 27, 30, 34, 38, 42, 45, 48, 52, 56, 60, 63, 66, 70, 74, 79, 83, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 133, 137, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 187, 191, 196, 200, 204, 208, 212, 216, 220, 224, 228
Offset: 0

Views

Author

Clark Kimberling, Feb 21 2018

Keywords

Comments

From the Bode-Harborth-Kimberling link:
a(n) = b(n-1) + b(n-2) + b(n-3) 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(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

Crossrefs

Cf. A022424, A299497.

Programs

  • Mathematica
    mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 3; a[1] = 4; a[2] = 5; b[0] = 1; b[1] = 2; 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}]    (* A299496 *)
Table[b[n], {n, 0, 100}]    (* A299497 *)

A299531 Solution a( ) of the complementary equation a(n) = 2*b(n-1) + b(n-2), where a(0) = 1, a(1) = 2; see Comments.

Original entry on oeis.org

1, 2, 11, 14, 17, 20, 23, 26, 29, 34, 38, 43, 47, 52, 56, 61, 65, 70, 74, 79, 83, 88, 92, 95, 98, 103, 107, 110, 115, 119, 122, 125, 130, 134, 137, 142, 146, 149, 152, 157, 161, 164, 169, 173, 176, 179, 184, 188, 191, 196, 200, 203, 206, 211, 215, 218, 223
Offset: 0

Views

Author

Clark Kimberling, Feb 21 2018

Keywords

Comments

From the Bode-Harborth-Kimberling link:
a(n) = 2*b(n-1) + b(n-2) for n > 1;
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

Crossrefs

Cf. A022424, A299532.

Programs

  • Mathematica
    mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;
a[n_] := a[n] = 2*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}]    (* A299531 *)
Table[b[n], {n, 0, 100}]    (* A299532 *)

A299532 Solution b( ) of the complementary equation a(n) = 2*b(n-1) + b(n-2), where a(0) = 1, a(1) = 2; see Comments.

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87
Offset: 0

Views

Author

Clark Kimberling, Feb 21 2018

Keywords

Comments

From the Bode-Harborth-Kimberling link:
a(n) = 2*b(n-1) + b(n-2) for n > 1;
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

Crossrefs

Cf. A022424, A299531.

Programs

  • Mathematica
    mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;
a[n_] := a[n] = 2*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}]    (* A299531 *)
Table[b[n], {n, 0, 100}]    (* A299532 *)

A299536 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-3), where a(0) = 1, a(1) = 2, a(2) = 3; see Comments.

Original entry on oeis.org

4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 18, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 34, 35, 36, 38, 40, 41, 42, 44, 46, 47, 49, 50, 52, 54, 55, 57, 58, 60, 62, 63, 64, 66, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 94, 96, 98, 99, 100
Offset: 0

Views

Author

Clark Kimberling, Feb 24 2018

Keywords

Comments

From the Bode-Harborth-Kimberling link:
a(n) = b(n-1) + b(n-3) for n > 3;
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(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

Crossrefs

Cf. A022424, A022427 (complement).

Programs

  • Mathematica
    mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 2; a[2] = 3; b[0] = 4; b[1] = 5;
a[n_] := a[n] = b[n - 1] + 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}]    (* A022427 *)
Table[b[n], {n, 0, 100}]    (* A299536 *)
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