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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A299411 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 2, a(1) = 3; see Comments.

Original entry on oeis.org

1, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 19, 21, 22, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 58, 59, 61, 62, 64, 66, 67, 69, 70, 72, 73, 75, 76, 78, 79, 81, 82, 84, 85, 87, 88, 90, 91, 93, 94, 96, 97, 99, 100
Offset: 0

Views

Author

Clark Kimberling, Feb 14 2018

Keywords

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

Crossrefs

Cf. A022424, A022426.

Programs

  • Mathematica
    mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 2; a[1] = 3; b[0] = 1; b[1] = 4;
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}]  (* A022426 *)
Table[b[n], {n, 0, 100}]  (* A299411 *)

A299416 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 3, a(1) = 4; see Comments.

Original entry on oeis.org

3, 4, 3, 7, 11, 14, 17, 19, 22, 25, 28, 31, 34, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173
Offset: 0

Views

Author

Clark Kimberling, Feb 15 2018

Keywords

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

Crossrefs

Cf. A022424, A299417.

Programs

  • Mathematica
    mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 3; a[1] = 4; 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}]  (* A299416 *)
Table[b[n], {n, 0, 100}]  (* A299417 *)

A299417 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 3, a(1) = 4; see Comments.

Original entry on oeis.org

1, 2, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 37, 39, 40, 42, 43, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 63, 64, 66, 67, 69, 70, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99
Offset: 0

Views

Author

Clark Kimberling, Feb 15 2018

Keywords

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

Crossrefs

Cf. A022424, A299416.

Programs

  • Mathematica
    mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 3; a[1] = 4; 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}]  (* A299416 *)
Table[b[n], {n, 0, 100}]  (* A299417 *)

A299418 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 3, a(1) = 5; see Comments.

Original entry on oeis.org

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
Offset: 0

Views

Author

Clark Kimberling, Feb 15 2018

Keywords

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

Crossrefs

Cf. A022424, A299419.

Programs

  • 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 *)

A299419 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 3, a(1) = 5; see Comments.

Original entry on oeis.org

1, 2, 4, 7, 8, 9, 10, 12, 13, 14, 16, 18, 20, 21, 23, 24, 26, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 42, 43, 45, 46, 48, 49, 51, 52, 53, 55, 56, 58, 59, 61, 62, 64, 66, 67, 69, 70, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99
Offset: 0

Views

Author

Clark Kimberling, Feb 16 2018

Keywords

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

Crossrefs

Cf. A022424, A299418.

Programs

  • 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 *)

A299420 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 4, a(1) = 5; see Comments.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Feb 16 2018

Keywords

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

Crossrefs

Cf. A022424, A299421.

Programs

  • 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 *)

A299421 Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 4, a(1) = 5; see Comments.

Original entry on oeis.org

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
Offset: 0

Views

Author

Clark Kimberling, Feb 16 2018

Keywords

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

Crossrefs

Cf. A022424, A299420.

Programs

  • 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 *)

A299486 Solution a( ) of the complementary equation a(n) = b(n-1) + b(n-2) + b(n-3), where a(0) = 1, a(1) = 2, a(2) = 3; see Comments.

Original entry on oeis.org

1, 2, 3, 15, 18, 21, 24, 27, 30, 33, 36, 39, 43, 47, 52, 56, 61, 65, 70, 74, 79, 83, 88, 92, 97, 101, 106, 110, 115, 119, 123, 127, 131, 135, 139, 143, 147, 150, 154, 158, 162, 166, 170, 174, 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, A299487.

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; 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}]    (* A299486 *)
v = Table[b[n], {n, 0, 100}]    (* A299487 *)

A299487 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) = 3; see Comments.

Original entry on oeis.org

4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 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, 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, A299486.

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; 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}]    (* A299486 *)
v = Table[b[n], {n, 0, 100}]    (* A299487 *)

A299488 Solution a( ) 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

1, 2, 4, 14, 18, 21, 24, 27, 30, 33, 36, 40, 44, 48, 52, 56, 61, 65, 70, 74, 79, 83, 88, 92, 97, 101, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 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, A299489.

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 *)
Previous Showing 11-20 of 57 results. Next

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