Even-Odd Series Sum

Computer Science Level 2

The following iterative sequence is defined for the set of positive integers:

{ n = n 2 if n is even. n = 3 n + 1 if n is odd. \begin{cases} n = \dfrac n2 & \text{if }n \text{ is even.} \\ n = 3n + 1 & \text{if }n \text{ is odd.} \end{cases}

When the initial value of n n is 13 the following sequence is formed and converges at 1:

13 40 20 10 5 16 8 4 2 1 \begin{array} {c} 13 & 40 & 20 & 10 & 5 & 16 & 8 & 4 & 2 & 1\end{array}

What is the sum of all terms when n = 100 n=100 ?


The answer is 808.

A Former Brilliant Member by A Former Brilliant Member

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3 solutions

The computation can be easily done with a Microsoft Excel spreadsheet as follows. Enter at cell A1: "100", cell A2: "=IF(MOD(A1,2)=0,A1/2,3*A1+1)" and copy through to A26, that is until n = 1 n=1 . Then enter at cell A27: "=SUM(A1:A26)" to sum up all the n n 's.

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Same here !

Nikola Alfredi - 1 year, 4 months ago
Steven Chase
Feb 8, 2020 
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n = 100

sum = n
flag = 0

while flag == 0:

    if n%2 == 0:
        n = n/2
    else:
        n = 3*n + 1

    sum = sum + n

    if n == 1:
        flag = 1

print sum
# 808

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