every so often

19 Aug 2010 392 views
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photoblog image Ten


Fishing match 'peg' near Henley-on-Thames

comments (10)

  • Chris
  • Germany
  • 19 Aug 2010, 07:32
Did you know that Ten is a composite number, its proper divisors being 1, 2 and 5. Ten is the smallest noncototient, a number that cannot be expressed as the difference between any integer and the total number of coprimes below it.

Ten is the second discrete semiprime (2.5) and the second member of the (2.q) discrete semiprime family. Ten has an aliquot sum σ(n) of 8 and is accordingly the first discrete semiprime to be in deficit. All subsequent discrete semiprimes are in deficit. The aliquot sequence for 10 comprises five members (10,8,7,1,0) with this number being the second composite member of the 7-aliquot tree.

It is the aliquot sum of only one number the discrete semiprime 14.

Ten is a semi-meandric number.

Ten is the sum of the first three prime numbers, of the four first numbers (1 + 2 + 3 + 4), of the square of the two first odd numbers and also of the first four factorials (0! + 1! + 2! + 3!). Ten is the eighth Perrin number, preceded in the sequence by 5, 5, 7.

A polygon with ten sides is a decagon, and 10 is a decagonal number. But it is also a triangular number and a centered triangular number.

Ten is the number of n-Queens Problem solutions for n = 5
John Prior: Thanks Chris, I see you've moved to Germany which explains the organised attention to detail smile
  • zed
  • Australia
  • 19 Aug 2010, 08:09
There is an expression for Chris's comment....to much information smile
John Prior: Thanks Zed, no need for Wikipedia, although I haven't checked the source smile
  • bk
  • 19 Aug 2010, 08:45
As a German I have to say I like information, if it is 'too much information'. There can never be too much information. =)
And I'd like to add that French philosopher Auguste Comte (a Positivist) was quite keen on the number 10, too. Even developed a calender based on tens...
But, John, this is really beautiful. I whish you'd show us a coloured version. Now I keep wondering about the colourful (mis-)match of grass/hay and spray paint.
John Prior: Thanks BK, and I agree with you about information. I did start shooting numbers I came across at one point with the view to a collection.
If a 10 or 17year old with a spray can had done this it would be called vandalism.
John Prior: Thanks Sheila, perhaps depending on where it was done.
Chris lost me after the first few words. It's such a simple thing it makes a very good picture John.
John Prior: Thanks Brian, something of a record post, as Chris now seems to reside in Germany smile, my return visit comment was in German to make him feel at home.
I am totally lost with Chris's comment lol, but I bet the fishermen knew where they were smile
John Prior: Thanks Linda, so was Chris - he ended up in Germany smile
Ten is Ten, as far as I'm concerned..but now I'm totally confused.
John Prior: Thanks Ron, I was a bit surprised.
Chris can be a right boring old fart
John Prior: Thanks for visit Bill
  • Otto K.
  • United States
  • 19 Aug 2010, 23:22
cool find. nice in B&W.
John Prior: Thanks Otto
You keep your 10 ... I'll have £10 for a reasonably good bottle of French red.

;-) richard

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