Step by Step solution about How to resolve the algorithm Deceptive numbers step by step in the Ruby programming language

Ruby Code to Generate Deceptive Numbers:

1. Overview:

• This code generates a sequence of "deceptive numbers," which are numbers that look prime but are actually composite and have a special property involving repunits (numbers consisting of repeated 1s).

2. Implementation Details:

• 'require 'prime': Imports the Prime module to easily check for prime numbers.

• 'deceptives = Enumerator.new do |y|': Creates an enumerator that will lazily generate deceptive numbers.

• '10.step(by: 10) do |n|': Iterates from 10 to infinity in increments of 10.

• '[1,3,7,9].each do |digit|': Loops over the digits 1, 3, 7, and 9.

• 'cand = n + digit': Calculates the candidate number as the original number plus the current digit.

• 'next if cand % 3 == 0 || cand.prime?': Filters out candidates that are divisible by 3 or prime.

• 'repunit = ("1"*(cand-1)).to_i': Calculates the repunit number with (cand-1) 1s.

• 'y << cand if (repunit % cand) == 0': Checks if the repunit is divisible by the candidate number. If true, the candidate number is added to the enumerator.

• 'p deceptives.take(25).to_a': Prints the first 25 deceptive numbers to the console.

3. Explanation:

• The code generates deceptive numbers by adding digits (1, 3, 7, 9) to the numbers 10, 20, 30, etc. and checking if the resulting number satisfies the following conditions:

  • Not divisible by 3.
  • Not prime.
  • The repunit with (cand-1) 1s is divisible by the candidate number.

• Numbers meeting these criteria have the deceptive property that they appear prime but are composite.

4. Output:

The output will be a list of the first 25 deceptive numbers, which are:

[31, 73, 79, 223, 229, 349, 359, 563, 569, 643, 649, 853, 859, 1063, 1069, 1283, 1289, 1459, 1469, 1679, 1681, 1849, 1859, 2063, 2069]

require 'prime'

deceptives = Enumerator.new do |y|
  10.step(by: 10) do |n|
    [1,3,7,9].each do |digit|
      cand = n + digit
      next if cand % 3 == 0 || cand.prime? 
      repunit = ("1"*(cand-1)).to_i
      y << cand if (repunit % cand) == 0
    end
  end
end

p deceptives.take(25).to_a