About the Number 7 (seven)

This BAB was created on 7 July 2007 (or in MM/DD/YY format: 07/07/07).

Where were you at 07:07:07 on 07/07/07?

07/07/07 is a BAD (Basic Arithmetic Date) because the square root of seven times seven is seven. Note: we should not be using 2-digit years. For example, in the 20th century, 07/07/07 was 7 July 1907. Science fiction writer Robert Heinlein died during May of 1988, yet he was born on 07/07/07.

Here is some stuff about the number 7...

   7 is a number (natural, whole, counting, integer)
   7 is a digit
   7 is a prime number
   7 is an odd number
   7 squared is 49 and 7 cubed is 343 and 7^7 = 823,543
   sqrt(7) approximates 2.64575131
   log(7) approximates 0.84509804
   ln(7) approximates 1.94591015
   7! = factorial(7) = 5040
   7 in binary is 111
   0777 are default permissions on newly created Unix directories

Ignoring details, number 7 is a "lucky number."

While reading the Wikipedia webpage on the number 7, GDT learned that the number 7 is a "happy number." Happy numbers are defined as follows: "replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1."

   7^2 = 49
   4^2 + 9^2 = 16 + 18 = 97
   9^2 + 7^2 = 81 + 49 = 130
   1^2 + 3^2 + 0^2 = 1 + 9 = 10
   1^2 + 0^2 = 1

By default, one is happy. Other happy numbers are 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, and so on.

RoadHacker has driven on IL Hwy-7 and OH Hwy-7.

Students found 7 MPH speed limit signs at Casino Arizona and inside an ASU parking garage. TempeHiker found a 7 MPH speed limit sign at Dobson High School in Mesa.

In a nutshell, although odd, the number 7 is prime, happy and lucky.

Update::2009.07.08

A lot of funtionality was added to the MathBabbler Number Analyst (MBNA) since this nBAB was created. Here is updated MBNA output about the number 7.

   MathBabbler Number Analyst (MBNA) output:
   =========================================
   7 is a natural, whole, integer
   7 is odd
   7 proper divisors are: 1,
   7 is deficient (sum of divisors is 1)
   7 is happy
   7 is a Harshad number
   7 is prime
   ...Cousin prime with 11
   ...Cousin prime with 3
   ...Safe prime with 3
   ...Sexy prime with 13
   ...Twin prime with 5
	...OEIS:002145 (4n+3; n=1)
   ...prime triplet {5, 7, 11}
   ...prime triplet {7, 11, 13}
   ...prime quadruplet {5, 7, 11, 13}
   7 is undulating
   7 is palindromic
   7 is repdigit in base-10
   7 is a Padovan number(4+3)
   7 is a lucky number
   7 in octal is 07
   7 in hexadecimal is 0x7
   7 in binary is 111 (is odious)
   7 nearest square numbers: -3...2 (4...9 [3])
   sqrt(7) = 2.64575
   ln(7) = 1.94591
   log(7) = 0.845098
   7 reciprocal is .14285714285714285714285714285714
   7! is 5040
   7 is 2.22817 Pi years
   7 is 0 score and 7 years
   7 written as a Roman numeral is VII

MathBabbler decided to update this nBAB about the number 7 after he received the following information.

   Michael Jackson signed his will on 7/7/02.
   Michael Jackson's memorial was on 7/7/09 exactly 
   ...7 years after the will was signed.
   Michael Jackson's two biggest hits -- "Black & White" 
   and "Billie Jean" -- were each #1 for 7 weeks.
   Michael Jackson's three biggest albums -- "Thriller," "Bad" 
   ...and "Dangerous" -- each produced 7 top 40 hits.
   Michael Jackson was the 7th of 9 children.
   Michael Jackson was born in 1958 ... 19 + 58 = 77
   Michael Jackson died on the 25th ... 2 + 5 = 7
   Michael Jackson has 7 letters in his first and last name.

   [source: TMZ.com]

[WolframAlpha.com] 7-sided polygons are regular heptagons.

[NumberGossip.com] 7 is a narcissistic number. The Wikipedia says a narcissistic number is a "number that in a given base is the sum of its own digits to the power of the number of digits."

OEIS.org::id:A005188

First few narcissistic numbers...

   1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 
   9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 
   9926315, 24678050, 24678051, 88593477, 146511208, 472335975, 
   534494836, 912985153, 4679307774, 32164049650, 32164049651...

Let's confirm that 153 and 370 are narcissistic numbers...

   153 has 3-digits; 1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153

   370 has 3-digits; 3^3 + 7^3 + 0^3 = 27 + 343 = 370

Update::2012.02.10

Numberphile posted 7 and Happy Numbers to their YouTube on 10 February 2012.

This nBAB for the number 7 was created on 7 July 2007 (07/07/07). The MBNA (MathBabbler Number Analyst) started checking for happy numbers on 8 March 2008.

Creator: Gerald D. Thurman [gthurman@gmail.com]
Created: 07 July 2007