### 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 )
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 