## Thursday, February 23, 2012

### the 25 challenge

good morning birthday girl!!!
today you are 25!!! 25 is a good number...

It is a square number, being 5² = 5 × 5. It is the smallest square that is also a sum of two (non-zero) squares: 25 = 3² + 4². Hence it often appears in illustrations of the Pythagorean theorem.
25 is a centered octagonal number, a centered square number, and an automorphic number.
25 per cent means one quarter.
25 has an aliquot sum of 6 and number 6 is the first (or smallest) number to have an aliquot sequence that does not culminate in 0 through a prime. Twenty-five is the aliquot sum of three integers; 95, 119, and 143. Twenty-five is the second composite member of the 6-aliquot tree.
It is the smallest base 10 Friedman number as it can be expressed by its own numbers: 5².
It is also a Cullen number. 25 is the smallest pseudoprime satisfying the congruence 7n = 7 mod n.
25 is the smallest aspiring number — a composite non-sociable number whose aliquot sequence does not terminate.
According to the Shapiro inequality, 25 is the least odd integer n such that there exist $x_1, x_2, \dots, x_n$ such that
$\sum_{i=1}^{n} \frac{x_i}{x_{i+1}+x_{i+2}} < \frac{n}{2}$
where xn + 1 = x1,xn + 2 = x2.
Within base 10 one can readily test for divisibility by 25 by seeing if the last two digits of the number match 25, 50, 75 or 00.
25 and 49 are the only perfect squares in the following list:
13,25,37,49,511,613,715,817,919,1021,1123,1225,1327,1429...etc.
The formula in this list can be described as 10n * Z + (2Z + 1) where n clearly depends on the number of digits in Z and in 2Z+1.
In base 30, 25 is a 1-automorphic number (displayed as the numeral 'P' or 'R' dependant on the chosen digit set), and in base 10 a 2-automorphic number.

25 is The atomic number of manganese

you see, turning 25 this year is so great...good things will come when carrying around a number like 25 for your age!!
lol, I know...I am truly brilliant, aren't I? to know all of these things, especially mathematic things, about the number 25? noooo...Ringo didn't tell me these facts (what do bet he knows all of them off the top of his head, though?) actually these facts came from here (proving I am only clever when it comes to searching for things on the internet!)

happy 25th birthday, dear sweet friend of mine!! soooo, i have a birthday challenge for you, since I won't be there to spend it with you....
step outside your room...see all of those balloons? (hahahahahahaha and now you are wondering how on earth those got there w/o you hearing them being delivered aren't you?!) there are 25 to be exact...and guess what's in each of them!?! $1.$25 total.  I had considered $25 in quarters... now, here is your challenge... you must find the best-ever find for$25 and post about it on your blog (so I can feel like I am there celebrating with you!!!) and i'll post/link it here...flea finds with V....or post a series of your choices and i'll guess what you chose? LOL...and you don't have to do it today...or at your usual flea...but you have to do it before we both see each other again!!!! i wish i was with you and we could first stop at coal creek, have a cuppa joe, chat about everything and nothing all at the same time...discuss our latest projects, how we plan to help the hurting of the world, our next moves, people that annoy us, people that we love...lol...and then, we would waste away the day shopping for the perfect \$3 find (lol that typcially comes from change in our purses!), it's truly a drug isn't it? LOL remember when we walked out of that shop after only being able to spend 30minutes absorbing it?
ok, happy happy birthday! i hope your birthday is splendid and that 25, the perfect square, is the perfect NON-square year for you!! because everything is always out of the box for you...just the way it's supposed to be!!!