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message 51:
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[deleted user]
(new)
Dec 10, 2014 09:50PM
I wonder why there appear to be falling standards in the education of what I call recreational mathematics...
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Just imagine next week's math test...12. What are happy prime numbers?
The number of digits in an integer is the number of numbers in some base (usually 10) required to represent it. The numbers 1 to 9 are therefore single digits, while the numbers 10 to 99 are double digits. Terms such as "double-digit inflation" are occasionally encountered, although this particular usage has thankfully not been needed in the U.S. for some time. The number of base- digits in a number can be calculated as
(1)
where is the floor function. For , the formula becomes
(2)
The number of digits in the number represented in base is given by the Mathematica function DigitCount[n, b, d], with DigitCount[n, b] giving a list of the numbers of each digit in . The total number of digits in a number is given by IntegerLength[n, b].
The positive integers with distinct base-10 digits are given by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, ... (OEIS A010784). The number of -digit integers is given by
(3)
(4)
(5)
(6)
where is a Pochhammer symbol. For , 2, ..., the first few values are 9, 81, 648, 4536, 27216, 136080, 544320, 1632960, 3265920, and 3265920 (OEIS A073531). There are therefore exactly
(7)
(8)
such numbers (Pondiczery 1975-a pseudonym for Ralph P. Boas; Foregger 1976), the largest of which is 9876543210.
The sums of the reciprocals of these 8877690 integers (Pondiczery 1975, Foregger 1976) is a rational number with numerator having 14816583 digits and denominator having 14816582 digits and given by
(9)
(10)
(OEIS A117914), computed by E. W. Weisstein on Apr. 1, 2006 using gridMathematica.
Numbers in base-10 which are divisible by their digits are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 111, 112, 115, 122, ... (OEIS A034838). Numbers which are divisible by the sum of their digits are called Harshad numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, ... (OEIS A005349). Numbers which are divisible by both their digits and the sum of their digits are 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 48, 111, 112, 126, 132, 135, 144, ... (OEIS A050104). Numbers which are equal to (i.e., not just divisible by) the product of their divisors and the sum of their divisors are called sum-product numbers and are given by 1, 135, 144, ... (OEIS A038369).
Lol! WE SHOULD EMAIL THAT TO A TEACHER jk Lol
I just found something else, Sexy Prime Numbers LOLOL
I just found something else, Sexy Prime Numbers LOLOL
I like the happy ones more... I'll stick with them
21 at the moment, I need to quit a few... XD
I just got a message from a friend: I got my dad to sign me into Hulu Plus (AKA I'M GOING TO STAY UP UNTILL THREE AM WATCHING DOCTOR WHO :D)
Oh Emily...
Oh Emily...
Ooh wow! I don't have Hulu Plus.
XD I'll try to watch an episode one day.
Watching Doctor is totally learning XD
Anyone open to RP with my twin characters?
That's awesome Dipper! That will totally be our Masthead photo :D
Fandoms can be movies too, right?
Great! I want to make a second character, but I don't know where it should be from...I don't get a chance to watch much except for Buffy the Vampire Slayer.
Of course! It can be anything!
Can we make an order for this? It might make it easier so everyone gets to post
We definitely should:
Analeese
Alex
Impala
Analeese
Alex
Impala
Lizzie, I'm ready to roleplay in Sophie's dorm if you want.
Do you want to post first or should I?
I'm still waiting for Nimue to be approved.
I just finished my Lily from the Giver character, whooo!
I think I'll take Eva from Vanderbilt and make her a daughter of Zeus
I think that's about right, considering her high and mighty personality. Plus, I'm too lazy to make my 100th rp charrie.
Hey Analeese!
I'm not on my Computer today, so I won't be making charries. :(
I'm not on my Computer today, so I won't be making charries. :(
Awww. :( Charries are fun, except for when you have a zillion and start to forget what you put in their personalities and history. I've done that before.
