About the Number 99 (ninety-nine)

MathBabbler made a joke about drinking during class about how the drinking age 18 when he went to college and that in Wisconsin they sang "999 Bottles of Beer on the Wall" instead of "99 Bottles of Beer on the Wall."

A few days earlier MathBabbler had posted nBABs for the numbers 94, 95, and 96. After posting the nBAB for the number 96, he observed that he had nBABs for all of the nineties excepted 98 and 99.

   MathBabbler Number Analyst (MBNA) output:
   =========================================
   99 is a natural, whole, integer
   99 is odd
   99 proper divisors are: 1,3,9,11,33,
   99 is deficient (sum of divisors is 57)
   99 is unhappy
   99 is not a Harshad number
   99 is not prime
   99 is undulating
   99 has the prime factors: 3*3*11
   99 in octal is 0143
   99 in hexadecimal is 0x63
   99 in binary is 1100011 (is evil)
   99 nearest square numbers: -18...1 (81...100 [10])
   sqrt(99) = 9.94987
   ln(99) = 4.59512
   log(99) = 1.99564
   99 reciprocal is .01010101010101010101010101010101
   99! is 9.33262e+155
   99 is 31.5127 Pi years
   99 is 4 score and 19 years
   99 written as a Roman numeral is XCIX

[Wikipedia] 99 is a Kaprekar number. "A Kaprekar number for a given base is a non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. For example, 297 is a Kaprekar number for base 10, because 297^2 = 88209, which can be split into 88 and 209, and 88 + 209 = 297."

   99^2 = 9801
   9801 split into two parts:  98  01
   98 + 01 = 99
   It's true!  99 is a Kaprekar number

Note: On 13 March 2009, the MBNA didn't check for Kaprekar numbers.

The first view Kaprekar numbers...

   1, 9, 45, 55, 99, 297, 703, 999 , 2223, 2728, 4879, 
   4950, 5050, 5292, 7272, 7777, 9999, 17344, 

OEIS.org::id:A006886

Back on 1 February 1999, long before GDT ever did a math class (i.e. pre-MathBabbler days), he wrote this Java program that prints the lyrics to "99 Bottles of Beer on Wall and speed at which the lyrics get printed slows down as the number of bottles of beer on the all approaches zero.

Update::2010.06.10

John Wooden, MathBabbler's favorite coach, died at the age of 99 on 4 June 2010.

The MBNA had new functionality added to it since this nBAB was created. The following is new MBNA output.

   MathBabbler Number Analyst (MBNA) output:
   =========================================
   99 is a natural, whole, integer
   99 is odd
   99 proper divisors are: 1,3,9,11,33,
   99 is deficient (sum of divisors is 57)
   99 is unhappy
   99 is not a Harshad number
   99 is not prime
   99 has the prime factors: 3*3*11 (sum=17)
   99 sum of prime factors is: 17
   99 is undulating
   99 is palindromic
   99 is repdigit in base-10
   99 is a lucky number
   99 in octal is 0143
   99 in hexadecimal is 0x63
   99 in binary is 1100011 (is evil)
   99 nearest square numbers: -18...1 (81...100 [10])
   sqrt(99) = 9.94987
   ln(99) = 4.59512
   log(99) = 1.99564
   99 reciprocal is .01010101010101010101010101010101
   99! is 9.33262e+155
   99 is 31.5127 Pi years
   99 is 4 score and 19 years
   99 written as a Roman numeral is XCIX
   99 = 50^2 - 49^2 and 50 + 49 = 99

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 13 March 2009

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