Numerical significance

Anyone care to guess the significance of these #'s ?
1111, 1001, 906, 609, 808, 818, 619, 916, 111

Such numbers are the "same" if read right-side up or up-side down.

Originally posted by twilight2007
Such numbers are the "same" if read right-side up or up-side down.

BOO YA

Here is a harder one (I think): Anyone care to guess the significance of these #'s ?

1048575, 255, 1, 8191

(the order of the numbers is irrelevant)

There is more than one way of answering this depending on how you look at it.

Originally posted by Andrew Hamilton
Here is a harder one (I think): Anyone care to guess the significance of these #'s ?

1048575, 255, 1, 8191

(the order of the numbers is [b]irrelevant)

There is more than one way of answering this depending on how you look at it.[/b]

One off 2^n, where n is some integer?

Originally posted by FabianFnas
One off 2^n, where n is some integer?

Correct: (2^n)-1

Also, if you convert any of these numbers to binary numbers, they will consist of all digit 1’s with no digit 0’s.
I find that this is on a very rare occasion useful to know when I am designing my software.

Originally posted by Andrew Hamilton
Correct: (2^n)-1

Also, if you convert any of these numbers to binary numbers, they will consist of all digit 1’s with no digit 0’s.
I find that this is on a very rare occasion useful to know when I am designing my software.

My assembler programming background helped me a little...

Here's a nice one. Compute the next one in the row:

1 4 27 3125 16777216

It would be 11^11, which is approx. 3.028751066x10^14.

Originally posted by KazetNagorra
Here's a nice one. Compute the next one in the row:

1 4 27 3125 16777216

shouldn't it be 13^13? the elements of the sequence are (n^n) where n is a member of the fibonacci sequence: 1^1, 2^2, 3^3, 5^5, 8^8, ...

Indeed, 13^13

Originally posted by KazetNagorra
Here's a nice one. Compute the next one in the row:

1 4 27 3125 16777216

1 4 27 3125 16777216 302875106592253 5842587018385982521381124421 ...

All these sequences have something simple in common -so what is it and how does each sequence continue? And can you add an example of another sequence to this list?

4, 20…

3, 12, 156, 24492, ….

2, 6, 30, 930, …..

1, 2, …..

0.5, 0.75, 1.3125, ….

0, 0, 0, 0, ….

-0.5, -0.25, -0.1875, …..

-1, 0, …..

-2, 2, ….

-3, 6, …..

-4, 12….

Wow...for some reason I thought 5 + 8 = 11...

Anyways...this problem is difficult since I can't use subscripts, but I'll try my best (and not make a simple mistake).

The pattern is (number)(number+1) = next number. The first numbers are decreasing by one as you go down. The next sequence (down) would be -5, 20, 420, ...

If I'm correct, then the third line is flawed; it should be 2, 6, 42, ...

Originally posted by Andrew Hamilton

2, 6, 30, 930, …..

My apologies: as twilight2007 correctly pointed out, this sequence should have been:

2, 6, 42, 1866 ...

and NOT: 2, 6, 30, 930, …..