Trollathon #1.3 : A Sum and A Function

Level 2

Let $A = 2 + 3 + ... + 23$

Answer = $A - p(p(p(p(2) + 1)))$

Hint : $p(1) = 2, p(3) = 5, p(5) = 11$ .

The answer is 41.

1 solution

Zi Song Yeoh
Apr 2, 2014

Firstly, one notes that $p(n)$ denotes the nth prime. So, $p(p(p(p(2) + 1))) = 59$ . The more difficult part is the sum. One obviously would think it is the sum of all integers from 2 to 23, but you discovered that it is wrong after submitting. One notes that this problem is about primes and suspect that it is the sum of all primes from 2 to 23, which gives $100$ . So, the answer is $100 - 59 = \boxed{41}$ .

Bad question, I considered $p(x)$ as the minimum value of the closest prime to $2x$ , so

$\begin{aligned} p(2) + 1 & = & 3 + 1 = 4 \\ p(p(2) + 1) & = & p(4) = 7 \\ p(p(p(2) + 1)) & = & p(7) = 13 \\ p(p(p(p(2) + 1))) & = & p(13) = 23 \\ \end{aligned}$

So the answer can also be $100 - 23 = \boxed{77}$

Pi Han Goh - 7 years, 2 months ago

LOL

Zi Song Yeoh - 7 years, 2 months ago

this problem really tolled me up

Kishlaya Jaiswal - 7 years, 2 months ago

Shouldn't it be trolled me up?

Ameya Salankar - 7 years, 2 months ago

LOL I missed that essential 'r'

Kishlaya Jaiswal - 7 years, 2 months ago

Trollathon #1.3 : A Sum and A Function

The answer is 41.

1 solution

0 pending reports