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Solved: Can you find a formula or rule for the nth term of

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 48E Chapter 4.3

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 48E

Can you find a formula or rule for the nth term of a sequence related to the prime numbers or prime factorizations so that the initial terms of the sequence have these values?

a) 2, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13.....

b) 0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6.........

c)  1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1....

d) 1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0,-1, 1, 1.....

e) 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0.......

f) 4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369....

Step-by-Step Solution:

Step 1 :

In this problem we have to find a formula or rule for the nth term of a se­quence.

Given the sequence 2, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13.....

Rule of term is

Where “p” is the set of prime number.

Step 2 :

     (b) given the sequence 0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6......... 

The rule of term is

Where is the prime.

is the least prime factor of n.

Step 3 :

        (c)  given the sequence is  1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1....

The rule of term is

Step 4 of 6

Chapter 4.3, Problem 48E is Solved
Step 5 of 6

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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