Chapter 5, Problem 36CRP

Explanation of Solution

Sequence of positive integers with prime divisors 2 and 3 only:

• The first step to design an algorithm is to check the remainder that is obtained from dividing the number equal to zero.
• In the given case, check the divisibility with 2 and 3.
• The reason for choosing the number 2 and 3 is that both the numbers are mutually prime and on dividing the number with 2 or 3 the remainder obtained is 1.

Algorithm:

Number $\leftarrow$ 2

while (Number > 1)

(

temp $\leftarrow$ number

while (remainder (temp/2)$==0$)

(

temp $\leftarrow$ temp/2

)

while (remainder(temp/3)$==0$)

(

temp $\leftarrow$ temp/3

)

if (temp==1)

(

print number

)

Number $\leftarrow$ Number $+1$

)

Explanation:

• The algorithm checks for number 2 first.
• The code “while (remainder (temp/2)$==0$)” checks if number is dividable by 2.
  • If number is dividable by 2, the code “temp $\leftarrow$ temp/2” updates value of “temp”