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

Purpose: The Wolfram programming language code snippet you provided identifies and returns "gapful" numbers within a specified range. A gapful number is a number whose first and last digits form a divisor of the number itself.

Breakdown:

ClearAll[GapFulQ]: Clears any previous definitions of a function named GapFulQ.

GapFulQ[n_Integer]:

• Defines a function that takes a positive integer as input.
• Converts the integer into a list of its digits using IntegerDigits.
• Extracts the first and last digits from the list and creates a new number from them using FromDigits.
• Checks if the original number is divisible by the first and last digit number.
• Returns True if it is divisible, and False otherwise.

i = 100: Initializes a variable i with the value 100.

res = {}: Initializes an empty list res that will store the gapful numbers found.

**While[Length[res] < 30, ... ]:

• Uses a While loop to continue searching for gapful numbers until res contains 30 elements.
• Inside the loop, the If statement checks if i is a gapful number using the GapFulQ function.
• If it is gapful, it appends the value of i to the res list.
• Then, i is incremented by 1 to check the next number.

The same loop is repeated two more times:

• Once with i starting at 10^6 and a target of finding 15 gapful numbers.
• Again with i starting at 10^9 and a target of finding 10 gapful numbers.

Finally, the program prints the list res for each of the three ranges.

ClearAll[GapFulQ]
GapFulQ[n_Integer] := Divisible[n, FromDigits[IntegerDigits[n][[{1, -1}]]]]
i = 100;
res = {};
While[Length[res] < 30,
 If[GapFulQ[i], AppendTo[res, i]];
 i++
 ]
res
i = 10^6;
res = {};
While[Length[res] < 15,
 If[GapFulQ[i], AppendTo[res, i]];
 i++
 ]
res
i = 10^9;
res = {};
While[Length[res] < 10,
 If[GapFulQ[i], AppendTo[res, i]];
 i++
 ]
res