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Add A000120 (#340)
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‎Algorithms.Tests/Sequences/OnesCountingSequenceTest.cs

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using System.Collections.Generic;
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using System.Linq;
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using System.Numerics;
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using Algorithms.Sequences;
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using FluentAssertions;
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using NUnit.Framework;
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namespace Algorithms.Tests.Sequences;
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[TestFixture]
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public class OnesCountingSequenceTest
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{
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/// <summary>
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/// <para>
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/// Values taken from http://oeis.org/A000120/b000120.txt.
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/// </para>
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/// <para>
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/// While the file contains 10,000 values, this only tests 1000.
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/// </para>
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/// </summary>
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private readonly BigInteger[] oeisValues = {
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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,
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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,
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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,
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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,
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3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5,
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6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4,
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4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5,
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6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5,
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3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3,
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4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6,
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6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3,
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4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5,
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4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3,
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4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6,
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6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6,
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7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
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3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4,
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5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4,
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4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6,
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7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7,
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6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3,
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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,
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4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6,
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7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6,
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4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4,
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5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4,
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4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4,
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5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7,
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6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5,
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6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7,
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7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4,
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5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
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3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5,
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6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5,
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5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6,
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7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5,
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4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6,
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7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7,
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7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7,
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8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8,
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};
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/// <summary>
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/// <para>
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/// Performs number of ones in the binary representation of a BigInteger.
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/// </para>
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/// <para>
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/// This is used as a check to compare the provided values from OEIS.
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/// </para>
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/// </summary>
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/// <param name="i">BigInteger value to count 1s in</param>
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/// <returns>Number of 1s in binary representation of number.</returns>
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private int CountOnes(BigInteger i)
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{
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var temp = i;
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BigInteger remainder = 0;
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var result = 0;
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while (temp != BigInteger.Zero) {
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temp = BigInteger.DivRem(temp, 2, out remainder);
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result += remainder.IsOne ? 1 : 0;
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}
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return result;
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}
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[Test]
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public void Count1000()
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{
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// Compare generated sequence against provided data
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var sequence = new OnesCountingSequence().Sequence.Take(oeisValues.Length);
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sequence.SequenceEqual(oeisValues).Should().BeTrue();
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}
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[Test]
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public void CompareAgainstCalculated()
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{
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// Calculate 1s in binary value the old fashioned way.
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var calculated = new List<BigInteger>();
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for (var i = 0; i < oeisValues.Length; i++) {
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calculated.Add(CountOnes(new BigInteger(i)));
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}
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calculated.SequenceEqual(oeisValues).Should().BeTrue();
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}
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}

‎Algorithms/Sequences/OnesCountingSequence.cs

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using System.Collections.Generic;
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using System.Numerics;
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namespace Algorithms.Sequences;
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/// <summary>
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/// <para>
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/// 1's-counting sequence: number of 1's in binary expression of n.
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/// </para>
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/// <para>
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/// OEIS: https://oeis.org/A000120.
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/// </para>
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/// </summary>
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public class OnesCountingSequence : ISequence
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{
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/// <summary>
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/// <para>
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/// Gets the generated sequence of the 1's contained in the binary representation of n.
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/// </para>
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/// <para>
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/// The sequence is generated as follows.
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/// 1. The initial 0 value is provided.
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/// 2. A recursively generated sequence is iterated, starting with a length of 1 (i.e., 2^0),
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/// followed by increasing 2^x length values.
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/// 3. Each sequence starts with the value 1, and a targeted value of depths that it will recurse
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/// for the specific iteration.
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/// 4. If the call depth to the recursive function is met, it returns the value argument received.
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/// 5. If the call depth has not been met, it recurses to create 2 sequences, one starting with the
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/// value argument, and the following with the value argument + 1.
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/// 6. Using ':' as a visual separator for each sequence, this results in the following sequences
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/// that are returned sequentially after the initial 0.
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/// 1 : 1, 2 : 1, 2, 2, 3 : 1, 2, 2, 3, 2, 3, 3, 4.
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/// </para>
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/// <remarks>
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/// <para>
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/// This one comes from thinking over information contained within the COMMENTS section of the OEIS page.
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/// </para>
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/// <para>
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/// Using the comments provided by Benoit Cloitre, Robert G. Wilson v, and Daniel Forgues, the above
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/// algorithm was coded.
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/// </para>
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/// </remarks>
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/// </summary>
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public IEnumerable<BigInteger> Sequence
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{
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get
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{
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yield return 0;
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var depth = 0;
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while (true)
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{
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foreach (var count in GenerateFractalCount(BigInteger.One, depth))
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{
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yield return count;
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}
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depth++;
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}
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}
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}
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/// <summary>
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/// <para>
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/// Recursive function to generate sequences.
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/// </para>
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/// </summary>
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/// <param name="i">The value that will start off the current IEnumerable sequence.</param>
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/// <param name="depth">The remaining depth of recursion. Value of 0 is the stop condition.</param>
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/// <returns>An IEnumerable sequence of BigInteger values that can be iterated over.</returns>
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private static IEnumerable<BigInteger> GenerateFractalCount(BigInteger i, int depth)
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{
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// Terminal condition
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if (depth == 0)
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{
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yield return i;
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yield break;
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}
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foreach (var firstHalf in GenerateFractalCount(i, depth - 1))
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{
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yield return firstHalf;
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}
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foreach (var secondHalf in GenerateFractalCount(i + 1, depth - 1))
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{
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yield return secondHalf;
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}
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}
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}

‎README.md

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* [A000045 Fibonacci](./Algorithms/Sequences/FibonacciSequence.cs)
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* [A000079 Powers of 2](./Algorithms/Sequences/PowersOf2Sequence.cs)
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* [A000108 Catalan](./Algorithms/Sequences/CatalanSequence.cs)
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* [A000120 1's Counting](./Algorithms/Sequences/OnesCountingSequence.cs)
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* [A000142 Factorial](./Algorithms/Sequences/FactorialSequence.cs)
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* [A000215 Fermat Numbers](./Algorithms/Sequences/FermatNumbersSequence.cs)
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* [A000290 Squares](./Algorithms/Sequences/SquaresSequence.cs)

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