Question

hmmm..seems i found an interesting math problem:

3,435 = 3^3 + 4^4 + 3^3 + 5^5

That is, it equals the sum of its digits each raised to that digit's power.

Find the next larger number with the same property. For this problem, use the convention that (0)^(0) = 0.

Answer 1

You probably mean \(3435 = 3^3 + 4^4 + 3^3 + 5^5 \). Then is is known as PPDI.

Answer 2

Oops wrong term.

Answer 3

I knew this give me a mint.

Answer 4

okayyy :DDD

Answer 5

Perfect digit-to-digit invariant http://en.wikipedia.org/wiki/Perfect_digit-to-digit_invariant

Answer 6

ohh so the PDDI

Answer 7

Indeed.

Answer 8

Aha yes it's PDDI and the answer you are seeking is \(438579088 = 4^4 + 3^3 + 8^8 +5^5 + 7^7 + 9^9 + 0^0 + 8^8 + 8^8 \)

Answer 9

wow o.O how do you do it...

Answer 10

Its's also called Munchausen Number. I was trying to remember this term only.

Answer 11

hmm munchausen..is it somehow related to a muchausen syndrome that a patient copies other people to gain attention?

Answer 12

Lol, I have no idea.

Answer 13

Yes, a PDDI number is called a narcissistic number.

Answer 14

@eashmore: a PDDI number is NOT called a narcissistic number.

Answer 15

PPDI is a narcissistic or Armstrong number

Answer 16

Are you sure? http://www.magic-squares.net/narciss.htm

Answer 17

Pretty much

http://en.wikipedia.org/wiki/Narcissistic_number
http://mathworld.wolfram.com/NarcissisticNumber.html

Answer 18

I stand corrected. It seems that the citations on the wikipedia page for PDDI lied to me!

Answer 19

Wow, nice work everyone. @lgbasallote @eashmore @FoolForMath - I'll be honest, this is way above me, but I can still respect it ;)