$P$ Sequence..... $P$ for what?

Level pending

Consider a sequence $P(n)$ defined for positive integers. The sequence is:

$1,2,3,5,7,11,15,a,b$

What is the value of $(a,b)$ ?

Hint: Think about what $P$ stands for.

Both (23,31) and (22,30) can complete the sequence. No pattern in the sequence. (23,31) (22.30) Both (19,29) and (17,27) can complete the sequence. (20,20) (19,19) (19,29)

1 solution

Anandmay Patel
Oct 17, 2016

$P$ here,mean partitions(of natural numbers).Got some idea? [For more explanation,please view the comments below.]

I didnt get it! Explain please.

Yatin Khanna - 4 years, 7 months ago

$1.)$ Firstly,the immediate observation is starting with 1,and then adding $2^0$ to get the next number.Again add $2^0$ to get the next number.Now add $2^1$ to it to get the next number.Again add $2^1$ to get the next one.Then, $2^2$ , and likewise, to complete the sequence........

$2.)$ And,another very common pattern here is the sequence constructed by the partition function.If $P(x)$ is the output of a partition function by an input of $x$ ,then the sequence is: $P(2),P(3),P(4)......$ .

Got it?

Anandmay Patel - 4 years, 7 months ago

I would have agreed if it was 23, 31 or 22, 29; I dont get the logic of 30

Yatin Khanna - 4 years, 7 months ago

What partition??? Please explain clearly

Navneet Prabhat - 4 years, 7 months ago

https://brilliant.org/wiki/partition-of-an-integer/

Take a look at the wiki.

Anandmay Patel - 4 years, 7 months ago

P P P Sequence..... P P P for what?

1 solution

0 pending reports

$P$ Sequence..... $P$ for what?