diff --git a/sequence/SEQUENCES_LIST.md b/sequence/SEQUENCES_LIST.md index 72ea148..acf5899 100644 --- a/sequence/SEQUENCES_LIST.md +++ b/sequence/SEQUENCES_LIST.md @@ -11,68 +11,68 @@ List of implemented integer sequences. -| OEIS | Sequence Name | Sequence class name(s) | Reference | -|---------|----------------------------------|-----------------------------------------------------------|--------------------------------------------------| -| A000027 | The natural numbers | `A000027`, `PositiveIntegers`, `NaturalNumbers` | https://oeis.org/A000027 | -| A000032 | The Lucas numbers | `A000032`, `LucasNumbers` | https://oeis.org/A000032 | -| A000040 | The prime numbers | `A000040`, `PrimeNumbers`, `PositivePrimeNumbers` | https://oeis.org/A000040 | -| A000045 | The Fibonacci numbers | `A000045`, `FibonacciNumbers`, `FibonacciSequence` | https://oeis.org/A000045 | -| A000073 | The Tribonacci numbers | `A000073`, `TribonacciNumbers` | https://oeis.org/A000073 | -| A000078 | The Tetranacci numbers | `A000078`, `TetranacciNumbers` | https://oeis.org/A000078 | -| A000120 | Sequence A000120 | `A000120`, | https://oeis.org/A000120 | -| A000129 | The Pell numbers | `A000129`, `PellNumbers`, `LambdaNumbers` | https://oeis.org/A000129 | -| A000217 | The triangular numbers | `A000217`, `TriangularNumbers` | https://oeis.org/A000217 | -| A000290 | The square numbers | `A000290`, `SquareNumbers` | https://oeis.org/A000290 | -| A000326 | The pentagonal numbers | `A000326`, `PentagonalNumbers` | https://oeis.org/A000326 | -| A000384 | The hexagonal numbers | `A000384`, `HexagonalNumbers` | https://oeis.org/A000384 | -| A000566 | The heptagonal numbers | `A000566`, `HeptagonalNumbers` | https://oeis.org/A000566 | -| A000567 | The octagonal numbers | `A000567`, `OctagonalNumbers` | https://oeis.org/A000567 | -| A000931 | The Padovan numbers | `A000931`, `PadovanNumbers`, `PadovanSequence` | https://oeis.org/A000931 | -| A001045 | The Jacobsthal numbers | `A001045`, `JacobsthalNumbers`, `JacobsthalSequence` | https://oeis.org/A001045 | -| A001106 | The nonagonal numbers | `A001106`, `NonagonalNumbers` | https://oeis.org/A001106 | -| A001107 | The decagonal numbers | `A001107`, `DecagonalNumbers` | https://oeis.org/A001107 | -| A001228 | Orders of sporadic simple groups | `A001228` | https://oeis.org/A001228 | -| A001591 | The Pentanacci numbers | `A001591`, `PentanacciNumbers` | https://oeis.org/A001591 | -| A001592 | The Hexanacci numbers | `A001592`, `HexanacciNumbers` | https://oeis.org/A001592 | -| A001608 | Perrin numbers | `A001608`, `PerrinNumbers` | https://oeis.org/A001608 | -| A002203 | Companion Pell numbers | `A002203`, `CompanionPellNumbers`, `PellLucasNumbers` | https://oeis.org/A002203 | -| A002808 | The composite numbers | `A002808`, `CompositeNumbers`, `PositiveCompositeNumbers` | https://oeis.org/A002808 | -| A003173 | The Heegner numbers | `A003173`, `HeegnerNumbers` | https://oeis.org/A003173 | -| A003215 | The hex numbers | `A003215`, `HexNumbers`, `CenteredHexagonalNumbers` | https://oeis.org/A003215 | -| A005408 | The odd numbers | `A005408`, `OddNumbers` | https://oeis.org/A005408 | -| A007953 | The digit sum | `A007953`, `Digsum` | https://oeis.org/A007953 | -| A010060 | The Thue-Morse sequence | `A010060`, `ThueMorseSequence` | https://oeis.org/A010060 | -| A014551 | Jacobsthal-Lucas numbers | `A014551`, `JachobsthalLucasNumbers` | https://oeis.org/A014551 | -| A033999 | Sequence of powers of -1 | `A033999` | https://oeis.org/A033999 | -| A051624 | The dodecagonal numbers | `A051624`, `DodecagonalNumbers` | https://oeis.org/A051624 | -| A051682 | The hendecagonal numbers | `A051682`, `HendecagonalNumbers` | https://oeis.org/A051682 | -| A051865 | The tridecagonal numbers | `A051865`, `TridecagonalNumbers` | https://oeis.org/A051865 | -| A051866 | The tetradecagonal numbers | `A051866`, `TetradecagonalNumbers` | https://oeis.org/A051866 | -| A051867 | The pentadecagonal numbers | `A051867`, `PentadecagonalNumbers` | https://oeis.org/A051867 | -| A051868 | The hexadecagonal numbers | `A051868`, `HexadecagonalNumbers` | https://oeis.org/A051868 | -| A051869 | The heptadecagonal numbers | `A051869`, `HeptadecagonalNumbers` | https://oeis.org/A051869 | -| A051870 | The octadecagonal numbers | `A051870`, `OctadecagonalNumbers` | https://oeis.org/A051870 | -| A051871 | The enneadecagonal numbers | `A051871`, `EnneadecagonalNumbers` | https://oeis.org/A051871 | -| A051872 | The icosagonal numbers | `A051872`, `IcosagonalNumbers` | https://oeis.org/A051872 | -| A051873 | The icosihenagonal numbers | `A051873`, `IcosihenagonalNumbers` | https://oeis.org/A051873 | -| A051874 | The icosidigonal numbers | `A051874`, `IcosidigonalNumbers` | https://oeis.org/A051874 | -| A051875 | The icositrigonal numbers | `A051875`, `IcositrigonalNumbers` | https://oeis.org/A051875 | -| A051876 | The icositetragonal numbers | `A051876`, `IcositetragonalNumbers` | https://oeis.org/A051876 | -| A053735 | Sequence A053735 | `A053735` | https://oeis.org/A053735 | -| A053737 | Sequence A053737 | `A053737` | https://oeis.org/A053737 | -| A053824 | Sequence A053824 | `A053824` | https://oeis.org/A053824 | -| A053827 | Sequence A053827 | `A053827` | https://oeis.org/A053827 | -| A053828 | Sequence A053828 | `A053828` | https://oeis.org/A053828 | -| A053829 | Sequence A053829 | `A053829` | https://oeis.org/A053829 | -| A053830 | Sequence A053830 | `A053830` | https://oeis.org/A053830 | -| A079262 | The Octanacci numbers | `A079262`, `OctanacciNumbers` | https://oeis.org/A079262 | -| A087204 | Sequence A087204 | `A087204` | https://oeis.org/A087204 | -| A104144 | The Enneanacci numbers | `A104144`, `EnneanacciNumebrs` | https://oeis.org/A104144 | -| A122189 | The Heptanacci numbers | `A122189`, `HeptanacciNumbers` | https://oeis.org/A122189 | -| A128834 | Sequence A128834 | `A128834` | https://oeis.org/A128834 | -| A167149 | The myriagonal numbers | `A167149`, `MyriagonalNumbers` | https://oeis.org/A167149 | -| A214733 | Sequence A214733 | `A214733` | https://oeis.org/A214733 | -| - | The Collatz sequence | `CollatzSequence` | https://en.wikipedia.org/wiki/Collatz_conjecture | +| OEIS | Sequence Name | Sequence class name(s) | Reference | +|---------|----------------------------------|-----------------------------------------------------------|-------------------------------------------------------------| +| A000027 | The natural numbers | `A000027`, `PositiveIntegers`, `NaturalNumbers` | [A000027](https://oeis.org/A000027) | +| A000032 | The Lucas numbers | `A000032`, `LucasNumbers` | [A000032](https://oeis.org/A000032) | +| A000040 | The prime numbers | `A000040`, `PrimeNumbers`, `PositivePrimeNumbers` | [A000040](https://oeis.org/A000040) | +| A000045 | The Fibonacci numbers | `A000045`, `FibonacciNumbers`, `FibonacciSequence` | [A000045](https://oeis.org/A000045) | +| A000073 | The Tribonacci numbers | `A000073`, `TribonacciNumbers` | [A000073](https://oeis.org/A000073) | +| A000078 | The Tetranacci numbers | `A000078`, `TetranacciNumbers` | [A000078](https://oeis.org/A000078) | +| A000120 | Sequence A000120 | `A000120`, | [A000120](https://oeis.org/A000120) | +| A000129 | The Pell numbers | `A000129`, `PellNumbers`, `LambdaNumbers` | [A000129](https://oeis.org/A000129) | +| A000217 | The triangular numbers | `A000217`, `TriangularNumbers` | [A000217](https://oeis.org/A000217) | +| A000290 | The square numbers | `A000290`, `SquareNumbers` | [A000290](https://oeis.org/A000290) | +| A000326 | The pentagonal numbers | `A000326`, `PentagonalNumbers` | [A000326](https://oeis.org/A000326) | +| A000384 | The hexagonal numbers | `A000384`, `HexagonalNumbers` | [A000384](https://oeis.org/A000384) | +| A000566 | The heptagonal numbers | `A000566`, `HeptagonalNumbers` | [A000566](https://oeis.org/A000566) | +| A000567 | The octagonal numbers | `A000567`, `OctagonalNumbers` | [A000567](https://oeis.org/A000567) | +| A000931 | The Padovan numbers | `A000931`, `PadovanNumbers`, `PadovanSequence` | [A000931](https://oeis.org/A000931) | +| A001045 | The Jacobsthal numbers | `A001045`, `JacobsthalNumbers`, `JacobsthalSequence` | [A001045](https://oeis.org/A001045) | +| A001106 | The nonagonal numbers | `A001106`, `NonagonalNumbers` | [A001106](https://oeis.org/A001106) | +| A001107 | The decagonal numbers | `A001107`, `DecagonalNumbers` | [A001107](https://oeis.org/A001107) | +| A001228 | Orders of sporadic simple groups | `A001228` | [A001228](https://oeis.org/A001228) | +| A001591 | The Pentanacci numbers | `A001591`, `PentanacciNumbers` | [A001591](https://oeis.org/A001591) | +| A001592 | The Hexanacci numbers | `A001592`, `HexanacciNumbers` | [A001592](https://oeis.org/A001592) | +| A001608 | Perrin numbers | `A001608`, `PerrinNumbers` | [A001608](https://oeis.org/A001608) | +| A002203 | Companion Pell numbers | `A002203`, `CompanionPellNumbers`, `PellLucasNumbers` | [A002203](https://oeis.org/A002203) | +| A002808 | The composite numbers | `A002808`, `CompositeNumbers`, `PositiveCompositeNumbers` | [A002808](https://oeis.org/A002808) | +| A003173 | The Heegner numbers | `A003173`, `HeegnerNumbers` | [A003173](https://oeis.org/A003173) | +| A003215 | The hex numbers | `A003215`, `HexNumbers`, `CenteredHexagonalNumbers` | [A003215](https://oeis.org/A003215) | +| A005408 | The odd numbers | `A005408`, `OddNumbers` | [A005408](https://oeis.org/A005408) | +| A007953 | The digit sum | `A007953`, `Digsum` | [A007953](https://oeis.org/A007953) | +| A010060 | The Thue-Morse sequence | `A010060`, `ThueMorseSequence` | [A010060](https://oeis.org/A010060) | +| A014551 | Jacobsthal-Lucas numbers | `A014551`, `JachobsthalLucasNumbers` | [A014551](https://oeis.org/A014551) | +| A033999 | Sequence of powers of -1 | `A033999` | [A033999](https://oeis.org/A033999) | +| A051624 | The dodecagonal numbers | `A051624`, `DodecagonalNumbers` | [A051624](https://oeis.org/A051624) | +| A051682 | The hendecagonal numbers | `A051682`, `HendecagonalNumbers` | [A051682](https://oeis.org/A051682) | +| A051865 | The tridecagonal numbers | `A051865`, `TridecagonalNumbers` | [A051865](https://oeis.org/A051865) | +| A051866 | The tetradecagonal numbers | `A051866`, `TetradecagonalNumbers` | [A051866](https://oeis.org/A051866) | +| A051867 | The pentadecagonal numbers | `A051867`, `PentadecagonalNumbers` | [A051867](https://oeis.org/A051867) | +| A051868 | The hexadecagonal numbers | `A051868`, `HexadecagonalNumbers` | [A051868](https://oeis.org/A051868) | +| A051869 | The heptadecagonal numbers | `A051869`, `HeptadecagonalNumbers` | [A051869](https://oeis.org/A051869) | +| A051870 | The octadecagonal numbers | `A051870`, `OctadecagonalNumbers` | [A051870](https://oeis.org/A051870) | +| A051871 | The enneadecagonal numbers | `A051871`, `EnneadecagonalNumbers` | [A051871](https://oeis.org/A051871) | +| A051872 | The icosagonal numbers | `A051872`, `IcosagonalNumbers` | [A051872](https://oeis.org/A051872) | +| A051873 | The icosihenagonal numbers | `A051873`, `IcosihenagonalNumbers` | [A051873](https://oeis.org/A051873) | +| A051874 | The icosidigonal numbers | `A051874`, `IcosidigonalNumbers` | [A051874](https://oeis.org/A051874) | +| A051875 | The icositrigonal numbers | `A051875`, `IcositrigonalNumbers` | [A051875](https://oeis.org/A051875) | +| A051876 | The icositetragonal numbers | `A051876`, `IcositetragonalNumbers` | [A051876](https://oeis.org/A051876) | +| A053735 | Sequence A053735 | `A053735` | [A053735](https://oeis.org/A053735) | +| A053737 | Sequence A053737 | `A053737` | [A053737](https://oeis.org/A053737) | +| A053824 | Sequence A053824 | `A053824` | [A053824](https://oeis.org/A053824) | +| A053827 | Sequence A053827 | `A053827` | [A053827](https://oeis.org/A053827) | +| A053828 | Sequence A053828 | `A053828` | [A053828](https://oeis.org/A053828) | +| A053829 | Sequence A053829 | `A053829` | [A053829](https://oeis.org/A053829) | +| A053830 | Sequence A053830 | `A053830` | [A053830](https://oeis.org/A053830) | +| A079262 | The Octanacci numbers | `A079262`, `OctanacciNumbers` | [A079262](https://oeis.org/A079262) | +| A087204 | Sequence A087204 | `A087204` | [A087204](https://oeis.org/A087204) | +| A104144 | The Enneanacci numbers | `A104144`, `EnneanacciNumebrs` | [A104144](https://oeis.org/A104144) | +| A122189 | The Heptanacci numbers | `A122189`, `HeptanacciNumbers` | [A122189](https://oeis.org/A122189) | +| A128834 | Sequence A128834 | `A128834` | [A128834](https://oeis.org/A128834) | +| A167149 | The myriagonal numbers | `A167149`, `MyriagonalNumbers` | [A167149](https://oeis.org/A167149) | +| A214733 | Sequence A214733 | `A214733` | [A214733](https://oeis.org/A214733) | +| - | The Collatz sequence | `CollatzSequence` | [Collatz](https://en.wikipedia.org/wiki/Collatz_conjecture) | ## Generalised integer sequences @@ -81,13 +81,13 @@ List of implemented integer sequences. List of implemented generalised integer sequences. -| Sequence Name | Sequence class name(s) | Reference | -|--------------------------------|-----------------------------|--------------------------------------------------------------------| -| The constant sequence | `ConstantSequence` | - | -| The digit sum sequence | `DigitSumSequence` | https://mathworld.wolfram.com/DigitSum.html | -| The generalised Nexus numbers | `GeneralisedNexusNumbers` | https://mathworld.wolfram.com/NexusNumber.html | -| High order Fibonacci numbers | `HighOrderFibonacciNumbers` | https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers | -| The Lucas sequence U_n | `LucasSequenceU` | https://en.wikipedia.org/wiki/Lucas_sequence | -| The Lucas sequence V_n | `LucasSequenceV` | https://en.wikipedia.org/wiki/Lucas_sequence | -| The primes of a given sequence | `PrimesOfSequence` | - | -| The polygonal numbers | `PolygonalNumbers` | https://en.m.wikipedia.org/wiki/Polygonal_number | +| Sequence Name | Sequence class name(s) | Reference | +|--------------------------------|-----------------------------|---------------------------------------------------------------------------------------------| +| The constant sequence | `ConstantSequence` | - | +| The digit sum sequence | `DigitSumSequence` | [Digit Sum](https://mathworld.wolfram.com/DigitSum.html) | +| The generalised Nexus numbers | `GeneralisedNexusNumbers` | [Nexus Number](https://mathworld.wolfram.com/NexusNumber.html) | +| High order Fibonacci numbers | `HighOrderFibonacciNumbers` | [Generalized Fubonacci](https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers) | +| The Lucas sequence U_n | `LucasSequenceU` | [Lucas Sequence](https://en.wikipedia.org/wiki/Lucas_sequence) | +| The Lucas sequence V_n | `LucasSequenceV` | [Lucas Sequence](https://en.wikipedia.org/wiki/Lucas_sequence) | +| The primes of a given sequence | `PrimesOfSequence` | - | +| The polygonal numbers | `PolygonalNumbers` | [Polygonal Number](https://en.m.wikipedia.org/wiki/Polygonal_number) |