Step by Step solution about How to resolve the algorithm Cullen and Woodall numbers step by step in the Mathematica/Wolfram Language programming language

The provided Wolfram code snippet defines two functions, CullenNumber and WoodallNumber, and uses them to find the first five prime Cullen numbers and the first 12 prime Woodall numbers.

Here's a detailed breakdown of the code:

1. Function Definitions:

   • CullenNumber[n]: This function calculates the Cullen number for a given integer n. The Cullen number is defined as n * 2^n + 1.
   • WoodallNumber[n]: This function calculates the Woodall number for a given integer n. The Woodall number is defined as n * 2^n - 1.

2. Listable Attributes: The Listable attribute is set for both CullenNumber and WoodallNumber functions. This attribute allows these functions to be applied to lists or arrays element-wise.

3. Finding Prime Cullen Numbers: The code finds the first five prime Cullen numbers using a loop:

   • It starts with i = 1 and increments it until it finds five prime Cullen numbers.
   • For each i, it calculates the corresponding Cullen number CullenNumber[i] and checks if it is prime using PrimeQ[CullenNumber[i]].
   • If the Cullen number is prime, it appends the value of i to the list cps (Cullen Prime Sequence).
   • The loop breaks when the length of cps reaches 5, indicating that five prime Cullen numbers have been found.

4. Finding Prime Woodall Numbers: The code follows a similar process to find the first 12 prime Woodall numbers:

   • It starts with i = 1 and increments it until it finds 12 prime Woodall numbers.
   • For each i, it calculates the corresponding Woodall number WoodallNumber[i] and checks if it is prime using PrimeQ[WoodallNumber[i]].
   • If the Woodall number is prime, it appends the value of i to the list wps (Woodall Prime Sequence).
   • The loop breaks when the length of wps reaches 12, indicating that 12 prime Woodall numbers have been found.

5. Printing the Results: Finally, the code prints the lists cps and wps to display the first five prime Cullen numbers and the first 12 prime Woodall numbers, respectively.

ClearAll[CullenNumber, WoodallNumber]
SetAttributes[{CullenNumber, WoodallNumber}, Listable]
CullenNumber[n_Integer] := n 2^n + 1
WoodallNumber[n_Integer] := n 2^n - 1

CullenNumber[Range[20]]
WoodallNumber[Range[20]]

cps = {};
Do[
 If[PrimeQ[CullenNumber[i]],
  AppendTo[cps, i];
  If[Length[cps] >= 5, Break[]]
  ]
 ,
 {i, 1, \[Infinity]}
 ]
cps

wps = {};
Do[
  If[PrimeQ[WoodallNumber[i]],
   AppendTo[wps, i];
   If[Length[wps] >= 12, Break[]]
   ]
  ,
  {i, 1, \[Infinity]}
  ];
wps