Digitsum sequences (#42)

CHANGELOG.md

@@ -24,7 +24,17 @@ The version is represented by three digits: a.b.c.
 ## Unreleased
 
 ENHANCEMENT:
-- sequentium.sequence.sequences.explicit.py: add sequence A010060 (Thue-Morse Sequence)
+- sequentium.sequence.sequences.explicit: add sequence A010060 (Thue-Morse Sequence)
+- sequentium.sequence.sequences.explicit_generalised: add class DigitSumSequence (https://mathworld.wolfram.com/DigitSum.html)
+- sequentium.sequence.sequences.explicit: add sequence A000120 (Number of 1's in binary expansion of n)
+- sequentium.sequence.sequences.explicit: add sequence A053735 (Sum of digits of n written in base 3)
+- sequentium.sequence.sequences.explicit: add sequence A053737 (Sum of digits of n written in base 4)
+- sequentium.sequence.sequences.explicit: add sequence A053824 (Sum of digits of n written in base 5)
+- sequentium.sequence.sequences.explicit: add sequence A053827 (Sum of digits of n written in base 6)
+- sequentium.sequence.sequences.explicit: add sequence A053828 (Sum of digits of n written in base 7)
+- sequentium.sequence.sequences.explicit: add sequence A053829 (Sum of digits of n written in base 8)
+- sequentium.sequence.sequences.explicit: add sequence A053830 (Sum of digits of n written in base 9)
+- sequentium.sequence.sequences.explicit: add sequence A007953 (digit sum)
 
 ---
 

sequence/SEQUENCES_LIST.md

@@ -19,6 +19,7 @@ List of implemented integer sequences.
 | 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                         |
@@ -39,6 +40,7 @@ List of implemented integer sequences.
 | 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                         |
@@ -56,6 +58,13 @@ List of implemented integer sequences.
 | 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                         |
@@ -75,11 +84,10 @@ 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/sequences/integer/explicit.py

@@ -4,6 +4,7 @@
 from sequence.core.infinite_type import Explicit
 from sequence.core.utils.functions import digit_sum
 from sequence.sequences.integer.explicit_generalised import (
+    DigitSumSequence,
     PolygonalNumbers,
     GeneralisedNexusNumbers,
 )
@@ -25,6 +26,15 @@ def formula(self, index: int) -> int:
 NaturalNumbers = A000027
 
 
+class A000120(DigitSumSequence):
+    """Number of 1's in binary expansion of n (https://oeis.org/A000120)."""
+
+    sequence_name = "sequence A000120"
+
+    def __init__(self) -> None:
+        super().__init__(base=2)
+
+
 class A000217(PolygonalNumbers):
     """Triangular numbers (https://oeis.org/A000217)."""
 
@@ -171,6 +181,18 @@ def formula(self, index: int) -> int:
 OddNumbers = A005408
 
 
+class A007953(DigitSumSequence):
+    """Digital sum (i.e., sum of digits) of n (https://oeis.org/A007953)."""
+
+    sequence_name = "digsum"
+
+    def __init__(self) -> None:
+        super().__init__(base=10)
+
+
+Digsum = A007953
+
+
 class A010060(Explicit):
     """Thue-Morse sequence (https://oeis.org/A010060)."""
 
@@ -383,6 +405,69 @@ def __init__(self) -> None:
 IcositetragonalNumbers = A051876
 
 
+class A053735(DigitSumSequence):
+    """Sum of digits of n written in base 3 (https://oeis.org/A053735)."""
+
+    sequence_name = "sequence A053735"
+
+    def __init__(self) -> None:
+        super().__init__(base=3)
+
+
+class A053737(DigitSumSequence):
+    """Sum of digits of n written in base 4 (https://oeis.org/A053737)."""
+
+    sequence_name = "sequence A053737"
+
+    def __init__(self) -> None:
+        super().__init__(base=4)
+
+
+class A053824(DigitSumSequence):
+    """Sum of digits of n written in base 5 (https://oeis.org/A053824)."""
+
+    sequence_name = "sequence A053824"
+
+    def __init__(self) -> None:
+        super().__init__(base=5)
+
+
+class A053827(DigitSumSequence):
+    """Sum of digits of n written in base 6 (https://oeis.org/A053827)."""
+
+    sequence_name = "sequence A053827"
+
+    def __init__(self) -> None:
+        super().__init__(base=6)
+
+
+class A053828(DigitSumSequence):
+    """Sum of digits of n written in base 7 (https://oeis.org/A053828)."""
+
+    sequence_name = "sequence A053828"
+
+    def __init__(self) -> None:
+        super().__init__(base=7)
+
+
+class A053829(DigitSumSequence):
+    """Sum of digits of n written in base 8 (https://oeis.org/A053829)."""
+
+    sequence_name = "sequence A053829"
+
+    def __init__(self) -> None:
+        super().__init__(base=8)
+
+
+class A053830(DigitSumSequence):
+    """Sum of digits of n written in base 9 (htpps://oeis.org/A053830)."""
+
+    sequence_name = "sequence A053830"
+
+    def __init__(self) -> None:
+        super().__init__(base=9)
+
+
 class A167149(PolygonalNumbers):
     """Myriagonal numbers (https://oeis.org/A167149)."""
 

sequence/sequences/integer/explicit_generalised.py

@@ -2,9 +2,31 @@
 
 from sequence.core.mixin import MonotonicIncreasingMixin
 from sequence.core.infinite_type import Explicit
+from sequence.core.utils.functions import digit_sum
 from sequence.core.utils.validation import validate_positive_integer
 
 
+class DigitSumSequence(Explicit):
+    """
+    Class representing digit sum sequences
+
+    Attributes:
+        - base (int): The base of the number to sum the digits
+    """
+
+    sequence_name = "digit sum sequence"
+
+    def __init__(self, base: int) -> None:
+        super().__init__()
+        self.base = validate_positive_integer(integer=base)
+
+    def __contains__(self, item: Any) -> bool:
+        return True
+
+    def formula(self, index: int) -> int:
+        return digit_sum(number=index, base=self.base)
+
+
 class GeneralisedNexusNumbers(MonotonicIncreasingMixin, Explicit):
     """
     Class representing a sequence of Generalised Nexus Numbers (https://mathworld.wolfram.com/NexusNumber.html).

tests/sequence_test_suite.py

@@ -32,7 +32,7 @@ def test_is_finite(self) -> None:
         """Test if the sequence's finiteness matches the expected value."""
         if self.sequence.is_finite != self.is_finite:
             raise ValueError(
-                f"Expected {self.is_finite} as output of the method `is_finite`. " f"But got {self.sequence.is_finite}."
+                f"Expected {self.is_finite} as output of the method `is_finite`. But got {self.sequence.is_finite}."
             )
 
     def test_is_periodic(self) -> None:
@@ -73,15 +73,6 @@ def test_in_operator(self) -> None:
         if error_msg:
             raise ValueError(error_msg)
 
-    def test_not_in_operator(self) -> None:
-        """Test if elements not in the ground truth are correctly identified as not in the sequence."""
-        error_msg = ""
-        for element in range(len(self.ground_truth)):
-            if element not in self.ground_truth and (element not in self.sequence) is False:
-                error_msg += f"- The expression ({element} in sequence) must be False, but it is not.\n"
-        if error_msg:
-            raise ValueError(error_msg)
-
     def test_as_list(self) -> None:
         """Test if the as_list method returns the expected subsequence for various start and stop indices."""
         error_msg = ""

tests/tests_integer_sequences/test_explicit.py

@@ -8,6 +8,16 @@ class TestA000027(SequenceTestSuite):
     ground_truth = list(range(100))
 
 
+class TestA000120(SequenceTestSuite):
+    sequence = A000120()
+    sequence_name = "sequence A000120"
+    ground_truth = [
+        0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2,
+        3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3,
+        3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3,
+    ]
+
+
 class TestA000217(SequenceTestSuite):
     sequence = A000217()
     sequence_name = "triangular numbers"
@@ -107,6 +117,16 @@ class TestA005408(SequenceTestSuite):
     ground_truth = [2 * index + 1 for index in range(50)]
 
 
+class TestA007953(SequenceTestSuite):
+    sequence = A007953()
+    sequence_name = "digsum"
+    ground_truth = [
+        0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8,
+        9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 12, 13,
+        14, 15, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 8, 9, 10, 11, 12, 13, 14, 15,
+    ]
+
+
 class TestA010060(SequenceTestSuite):
     sequence = A010060()
     sequence_name = "Thue-Morse sequence"
@@ -116,6 +136,7 @@ class TestA010060(SequenceTestSuite):
         0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0
     ]
 
+
 class TestA014551(SequenceTestSuite):
     sequence = A014551()
     sequence_name = "Jacobsthal-Lucas numbers"
@@ -272,6 +293,76 @@ class TestA051876(SequenceTestSuite):
     ]
 
 
+class TestA053735(SequenceTestSuite):
+    sequence = A053735()
+    sequence_name = "sequence A053735"
+    ground_truth = [
+        0, 1, 2, 1, 2, 3, 2, 3, 4, 1, 2, 3, 2, 3, 4, 3, 4, 5, 2, 3, 4, 3, 4, 5, 4, 5, 6, 1, 2, 3, 2, 3, 4, 3, 4, 5, 2,
+        3, 4, 3, 4, 5, 4, 5, 6, 3, 4, 5, 4, 5, 6, 5, 6, 7, 2, 3, 4, 3, 4, 5, 4, 5, 6, 3, 4, 5, 4, 5, 6, 5, 6, 7, 4, 5,
+        6, 5, 6, 7, 6, 7, 8, 1, 2, 3, 2, 3, 4, 3, 4, 5, 2, 3, 4, 3, 4, 5, 4, 5, 6, 3, 4, 5, 4, 5, 6,
+    ]
+
+
+class TestA053737(SequenceTestSuite):
+    sequence = A053737()
+    sequence_name = "sequence A053737"
+    ground_truth = [
+        0, 1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 6, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 2, 3, 4, 5, 3,
+        4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 6, 7, 8, 9, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4,
+        5, 6, 4, 5, 6, 7, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 3, 4, 5, 6, 4, 5, 6, 7, 5,
+    ]
+
+
+class TestA053824(SequenceTestSuite):
+    sequence = A053824()
+    sequence_name = "sequence A053824"
+    ground_truth = [
+        0, 1, 2, 3, 4, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4,
+        5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9,
+        10, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 7, 8, 9, 10, 11, 4, 5, 6,
+    ]
+
+
+class TestA053827(SequenceTestSuite):
+    sequence = A053827()
+    sequence_name = "sequence A053827"
+    ground_truth = [
+        0, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 1,
+        2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 2,
+        3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10,
+    ]
+
+
+class TestA053828(SequenceTestSuite):
+    sequence = A053828()
+    sequence_name = "sequence A053828"
+    ground_truth = [
+        0, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 8, 3, 4, 5, 6, 7, 8, 9, 4, 5, 6, 7, 8, 9, 10, 5, 6,
+        7, 8, 9, 10, 11, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 8, 3, 4, 5, 6, 7, 8, 9, 4, 5, 6,
+        7, 8, 9, 10, 5, 6, 7, 8, 9, 10, 11, 6, 7, 8, 9, 10, 11, 12, 7, 8, 9, 10, 11,
+    ]
+
+
+class TestA053829(SequenceTestSuite):
+    sequence = A053829()
+    sequence_name = "sequence A053829"
+    ground_truth = [
+        0, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 2, 3, 4, 5, 6, 7, 8, 9, 3, 4, 5, 6, 7, 8, 9, 10, 4, 5, 6, 7, 8,
+        9, 10, 11, 5, 6, 7, 8, 9, 10, 11, 12, 6, 7, 8, 9, 10, 11, 12, 13, 7, 8, 9, 10, 11, 12, 13, 14, 1, 2, 3, 4, 5, 6,
+        7, 8, 2, 3, 4, 5, 6, 7, 8, 9, 3, 4, 5, 6, 7, 8, 9, 10, 4, 5, 6, 7, 8, 9, 10,
+    ]
+
+
+class TestA053830(SequenceTestSuite):
+    sequence = A053830()
+    sequence_name = "sequence A053830"
+    ground_truth = [
+        0, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3, 4, 5, 6, 7, 8, 9, 10, 11,
+        4, 5, 6, 7, 8, 9, 10, 11, 12, 5, 6, 7, 8, 9, 10, 11, 12, 13, 6, 7, 8, 9, 10, 11, 12, 13, 14, 7, 8, 9, 10, 11,
+        12, 13, 14, 15, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8, 9,
+    ]
+
+
 class TestA167149(SequenceTestSuite):
     sequence = A167149()
     sequence_name = "myriagonal numbers"

tests/tests_meta/test_scripts.py

@@ -53,14 +53,15 @@ def test_markdown() -> None:
 
     sequences_in_markdown_but_not_in_scripts = sequence_markdown.difference(sequence_scripts)
     error_msg = ""
-    if sequences_in_markdown_but_not_in_scripts != set():
+    sequences_in_markdown_but_not_in_scripts = {entry for entry in sequences_in_markdown_but_not_in_scripts if entry}
+    if len(sequences_in_markdown_but_not_in_scripts) > 0:
         error_msg += (
             f"The following sequences are in the SEQUENCE_LIST.md, "
             f"but are not implemented: {', '.join(list(sequences_in_markdown_but_not_in_scripts))}\n"
         )
 
     sequences_in_scripts_but_not_in_markdown = sequence_scripts.difference(sequence_markdown)
-    if sequences_in_scripts_but_not_in_markdown != set():
+    if len(sequences_in_scripts_but_not_in_markdown) > 0:
         error_msg += (
             f"The following sequences are implemented, "
             f"but are not in SEQUENCE_LIST.md: {', '.join(list(sequences_in_scripts_but_not_in_markdown))}"