Special whole numbers...

[fetofs]

Originally Posted by mfgoode

It's my turn again so here goes:
14833 (math)
Mally

14833=!8 (subfactorial again )

1006

P.S:Mally, I don't know what a 7-oct mean. You gave this property, so ou should know what it means!!!!

[xilman]

Originally Posted by fetofs

14833=!8 (subfactorial again )

1006

P.S:Mally, I don't know what a 7-oct mean. You gave this property, so ou should know what it means!!!!

Brightest supernova of the second millenium appeared the constellation of Lupus in 1006AD.


823543


Paul

[mfgoode]

Originally Posted by xilman

Brightest supernova of the second milenium appeared the constellation of Lupus in 1006AD.


823543


Paul

:surprised Thanks Paul for coming to the rescue. I thought as much as it rang a bell as a historical date.

I got my info from 'What's special about this number?' a URL given by Flatlander. Here is what it says

1006 has a cube that is a concatenation of other cubes.

On similar lines I arrive at
1006 as
1006 =9^3 + 6^3 + 4^3 - 3

To continue, Paul takes the stage:
823543.
Mally

[Richard Cameron]

823543 = 7^7

as 7^2 is one less than half of 100, I suspect this means its reciprocal is very interesting too...


2008. Clue: not the date

[mfgoode]

Originally Posted by Richard Cameron

823543 = 7^7

as 7^2 is one less than half of 100, I suspect this means its reciprocal is very interesting too...


2008. Clue: not the date

2008. Clue: not the date[/QUOTE]
Yes the reciprocal is very interesting as 1/49 =0.020408163265 ...
in which the powers of 2 appear in sequence, eventually overlapping so that the pattern, although still there, cannot be seen. Its period is cyclic and is 42.

Another interesting observation is that when Christ was asked by a disciple if he should forgive his enemies 7 times the reply was '70 * 7.'
Normally this comes to 70 * 7 =490 but the mystical meaning is 70 ^ 7
That is 823543 * 10 ^ 7.

2008: is a Kaprekar constant in base 3

666 : (scriptural ) and mathematical.
Mally

[mfgoode]

Originally Posted by mfgoode

2008. Clue: not the date

:.

2008: is a Kaprekar constant in base 3

666 : (scriptural ) and mathematical.

Mally [/QUOTE]
The kaprekar constant is 6147 so asfaik these numbers dont tally in base 3. Could someone please confirm and I will correct the error in the URL of Flatlander.
So the numbers remain
2008:

666:

Mally

[Richard Cameron]

Originally Posted by mf goode

The kaprekar constant is 6147 so asfaik these numbers dont tally in base 3. Could someone please confirm and I will correct the error in the URL of Flatlander.

some time ago I wrote:

Originally Posted by Richard Cameron

6174 is Kaprekar's constant for 4 digit numbers. I suppose I should add "in base ten".

2008 in base 3 is 2202101. 2221100 minus 0011222 is 2202101.

So 2008 is (a?) Kaprekar constant for 7-digit numbers, base 3.


Richard

[mfgoode]

:surprised Richard, you're a genius! You are one up on Kaprekar!
Thanks a million for this insight. I never considered this angle before though I have a faint recollection that 5 digit numbers in base ten have a kind of a cyclic constant considered by Kaprekar.
Well back to David Wells Penguin Dict. as I saw it in there.

FYI: my son in London has bought Wells' latest (June, 2005 ) which I ordered from Waterstones at Kensington called 'Prime Numbers' (~ 288 pages) which gives, on my review, on Amazon.com a page a fact on primes and their associates,pseudoprimes etc.

On his recent visit to Mumbai and Goa, he got me Dan Rockmore's 'Stalking the Riemann Hypothesis'. I still have a £10 gift voucher to utilise. Any recommendations in that price range?

I also got 'The little book of Bigger Primes' by P. Ribenboim recommended by Tony Rex. So I have a a lot of reading to catch up with.
Currently I am on 'Prime Obsession' by John Derbyshire recommended by Numbers.

666 (scriptural and mathematical)
Mally

[Richard Cameron]

since this thread has gone quiet

Originally Posted by Wikipedia

666 is an abundant number. It is the sum of the squares of the first seven prime numbers.

Since 36 is both square and triangular, 666 is the sixth number of the form n2(n2 + 1) / 2 (triangular squares) and the eighth number of the form n(n + 1)(n2 + n + 2) / 8 (doubly triangular numbers.)

I don't think the first property is very noteworthy: 666 is a multiple of 6 so its abundant. But the others are all good. "n2" is supposed to be "n squared" but i don't know how to change the font.

I'll leave the scriptural significance to someone else: I understand there is some debate over whether the number of the beast should in fact be 666 or 616. I even read somewhere that it was a reference to Plato's Republic and should really be 216.

Richard

[mfgoode]

:surprised Thank you Richard Cameron, those are very interesting properties from Wikipedia
Originally Posted by Wikipedia
666 is an abundant number. It is the sum of the squares of the first seven prime numbers.

Since 36 is both square and triangular, 666 is the sixth number of the form n2(n2 + 1) / 2 (triangular squares) and the eighth number of the form n(n + 1)(n2 + n + 2) / 8 (doubly triangular numbers.)

The scriptural ref:REV : 13 18 is very well known. I was merely emphasizing it.
Think about it, it has a lot of wisdom not known at all
by the many but only to a few masters in the world.

Math: 666 = 1^3 + 2 ^3 + 3^ 3 + 4^3 +5 ^3 +6^3 +5^3 +4^3 +....... 1^3.
666 = 6 * 111
111 = the magic constant of the 6*6 magic square and the total sum of the numbers in the square known as the 'square of the sun' is 666.
It is very difficult to construct a magic square 6*6 where the magic constant is 111 for the natural numbers. i.e. 1 to 36. Try it out. If you can get it in a month's time then you are pretty good for a 'magic square freak'

My number 43.

Mally

[Richard Cameron]

Originally Posted by mfgoode

My number 43.

Mally

The first ed of Wells lists 41 as the first 'uninteresting' number. 43 is the first natural number not in the book. 43 is of course in the second edition.

This is rather naughty of me, but a friend has just proposed

27,893,791,104,637,013,345,492,828,124

as a 'noteworthy' number. Its naughty cos i can't verify the property he's proposing for it!


Richard