Unique number?

Post by Mathedman
Consider the integer 3435.
Now to each digit place an exponent = to the digit and sum the new digits".
3^3 + 4^4 + 3^3 + 5^5
The sum is 3435 !!!

Yes, those numbers are called Munchausen numbers.

A Munchausen number is a natural number n the sum of whose digits (in base 10), each raised to the power of itself, equals n.
________________________________________________________ Gerard Schildberger

William Elliot

2017-09-14 04:48:29 UTC

Consider the integer 3435.
Now to each digit place an exponent =
to the digit and sum the new digits".
3^3 + 4^4 + 3^3 + 5^5
The sum is 3435 !!!

Yes, those numbers are called Munchausen numbers.
A Munchausen number is a natural number n the sum of whose digits
(in base 10), each raised to the power of itself, equals n.

What other Munchkins are there besides 1?

Gerard Schildberger

2017-09-14 06:31:01 UTC

Consider the integer 3435.
Now to each digit place an exponent =
to the digit and sum the new digits".
3^3 + 4^4 + 3^3 + 5^5
The sum is 3435 !!!

Yes, those numbers are called Munchausen numbers.
A Munchausen number is a natural number n the sum of whose digits
(in base 10), each raised to the power of itself, equals n.

What other Munchkins are there besides 1?

I can't speak for Munchkins, but as for Munchhausen numbers, it
depends on the words used to describe them.

1). A Munchausen number is a natural number N the sum of whose
digits (in base 10), each raised to the power of itself,
equals N, where 0^0 is defined to be zero. (Most purist
despise this definition.)

2). A Munchausen number is a natural number N the sum of whose
non-zero digits (in base 10), each raised to the power of
itself, equals N.

Using the 2nd definition, there is another number that fits the bill:
438579088
_____________________________________________ Gerard Schildberger

William Elliot

2017-09-15 03:36:23 UTC

Consider the integer 3435.
Now to each digit place an exponent =
to the digit and sum the new digits".
3^3 + 4^4 + 3^3 + 5^5
The sum is 3435 !!!

Yes, those numbers are called Munchausen numbers.
A Munchausen number is a natural number n the sum of whose digits
(in base 10), each raised to the power of itself, equals n.

What other Munchkins are there besides 1?

I can't speak for Munchkins, but as for Munchhausen numbers, it
depends on the words used to describe them.
1). A Munchausen number is a natural number N the sum of whose
digits (in base 10), each raised to the power of itself,
equals N, where 0^0 is defined to be zero. (Most purist
despise this definition.)
2). A Munchausen number is a natural number N the sum of whose
non-zero digits (in base 10), each raised to the power of
itself, equals N.
438579088

1 is another munchkin.

How many base 12 munchkins are there?
Is there, other than 1, at least one munchkin for each base?
All bases included, are there infinitely many munchkins?

Gerard Schildberger

2017-09-15 04:48:15 UTC

Consider the integer 3435.
Now to each digit place an exponent =
to the digit and sum the new digits".
3^3 + 4^4 + 3^3 + 5^5
The sum is 3435 !!!

Yes, those numbers are called Munchausen numbers.
A Munchausen number is a natural number n the sum of whose digits
(in base 10), each raised to the power of itself, equals n.

What other Munchkins are there besides 1?

I can't speak for Munchkins, but as for Munchhausen numbers, it
depends on the words used to describe them.
1). A Munchausen number is a natural number N the sum of whose
digits (in base 10), each raised to the power of itself,
equals N, where 0^0 is defined to be zero. (Most purist
despise this definition.)
2). A Munchausen number is a natural number N the sum of whose
non-zero digits (in base 10), each raised to the power of
itself, equals N.
438579088

1 is another munchkin.
How many base 12 munchkins are there?
Is there, other than 1, at least one munchkin for each base?
All bases included, are there infinitely many munchkins?

That are not an infinite number of Munchausen numbers for any base.

The Wikipedia article

https://en.wikipedia.org/wiki/Perfect_digit-to-digit_invariant

on perfect digit-to-digit invariant (PDDI) (also known as a Munchausen
number), in the section

Proof of finitude

shows that there is a finite number of Munchausen numbers in any base.
__________________________________________________ Gerard Schildberger

Barry Schwarz

2017-09-15 07:56:04 UTC

Consider the integer 3435.
Now to each digit place an exponent =
to the digit and sum the new digits".
3^3 + 4^4 + 3^3 + 5^5
The sum is 3435 !!!

Yes, those numbers are called Munchausen numbers.
A Munchausen number is a natural number n the sum of whose digits
(in base 10), each raised to the power of itself, equals n.

What other Munchkins are there besides 1?

I can't speak for Munchkins, but as for Munchhausen numbers, it
depends on the words used to describe them.
1). A Munchausen number is a natural number N the sum of whose
digits (in base 10), each raised to the power of itself,
equals N, where 0^0 is defined to be zero. (Most purist
despise this definition.)
2). A Munchausen number is a natural number N the sum of whose
non-zero digits (in base 10), each raised to the power of
itself, equals N.
438579088

1 is another munchkin.
How many base 12 munchkins are there?
Is there, other than 1, at least one munchkin for each base?
All bases included, are there infinitely many munchkins?

Read the Wikipedia article.

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Barry Schwarz

2017-09-14 09:03:46 UTC