49 (number)

49 (forty-nine) is the natural number following 48 and preceding 50.

In mathematics
Forty-nine is the square of the prime number 7|seven and hence the fourth non-unitary square prime of the form p2

49 has an aliquot sum of 8; itself a prime power, and hence an aliquot sequence of two composite members (49, 8, 7,1,0).

It appears in the Padovan sequence, preceded by the terms 21, 28, 37 (it is the sum of the first two of these).

Along with the number that immediately derives from it, 77, the only number under 100 not having its home prime known.

The smallest triple of three squares in arithmetic succession is (1,25,49), and the second smallest is (49,169,289).

49 is the smallest discriminant of a totally real cubic field.

49 and 94 are the only numbers below 100 whose all permutations are composites but they are not multiples of 3, repdigits or numbers which only have digits 0, 2, 4, 5, 6 and 8, even excluding the trivial one digit terms.

49 = 7^2 and 94 = 2 * 47

Decimal representation
The sum of the digits of the square of 49 (2401) is the square root of 49.

49 is the first square where the digits are squares. In this case, 4 and 9 are squares.

Reciprocal
The fraction $1⁄49$ is a repeating decimal with a period of 42:


 * $1⁄49$ = $\overline{0.|0204081632 6530612244 8979591836 7346938775 51}$ (42 digits repeat)

There are 42 positive integers less than 49 and coprime to 49. (42 is the period.) Multiplying 020408163265306122448979591836734693877551 by each of these integers results in a cyclic permutation of the original number:


 * 020408163265306122448979591836734693877551 &times; 2 = 040816326530612244897959183673469387755102
 * 020408163265306122448979591836734693877551 &times; 3 = 061224489795918367346938775510204081632653
 * 020408163265306122448979591836734693877551 &times; 4 = 081632653061224489795918367346938775510204

The repeating number can be obtained from 02 and repetition of doubles placed at two places to the right:

02  04     08       16         32           64            128              256                512                 1024                   2048 +                   ... -- 020408163265306122448979591836734693877551...0204081632...

because $1/49$ satisfies:
 * $$x = \frac{1}{50} + \frac{2x}{100} = \frac{1}{50}(1 + x)\, .$$

In chemistry

 * The atomic number of indium.
 * During the Manhattan Project, plutonium was also often referred to simply as "49". Number 4 was for the last digit in 94 (atomic number of plutonium) and 9 for the last digit in Pu-239, the weapon-grade fissile isotope used in nuclear bombs.

In astronomy

 * Messier object M49, a magnitude 10.0 galaxy in the constellation Virgo.
 * The New General Catalogue object NGC 49, a spiral galaxy in the constellation Cetus.

In religion

 * In Judaism: the number of days of the Counting of the Omer and the number of years in a Jubilee (biblical) cycle.
 * The number of days and night Siddhartha Gautama spent meditating as a holy man
 * In Buddhism, 49 days is one of the lengths of the intermediate state (bardo)

In sports

 * 49er, a member of the San Francisco 49ers team of the National Football League (United States football).
 * Arsenal had a 49-game unbeaten run between May 2003 and October 2004 until they lost to Manchester United, which is a national record in English football.
 * Rocky Marciano ended his boxing career as the only heavyweight champion with a perfect record—49 wins in 49 professional bouts, with 43 knockouts.
 * Indian Premier League cricket team Royal Challengers Bangalore holds the lowest ever team total in IPL history in the 2017 edition of IPL

In music

 * "49 Bye-Byes", a song on the self-titled album Crosby Stills and Nash
 * "Days of '49", a 19th century folk song about the California Gold Rush, recorded by Bob Dylan (on the album Self Portrait) and by many others
 * 49:00... Of Your Time/Life is a one-track solo album by Paul Westerberg.
 * In Blues music lore, it was at the junction of US Highway 49 and 61 in Clarksdale, Mississippi, that legendary bluesman Robert Johnson sold his soul to the devil in return for fame and success. In later years Howlin' Wolf immortalized the road in the song "Highway 49", originally written by Big Joe Williams.

In other fields
Forty-nine is:
 * HP-49 series is a Hewlett-Packard calculator
 * 49er, one who participated in the 1849 California Gold Rush.
 * The code for international direct dial phone calls to Germany
 * In the title of Thomas Pynchon's novel The Crying of Lot 49
 * In the title of the movies Ladder 49 and 49 Up
 * A 49 is a party after a powwow or any gathering of American Indians, held by the participants. It is also type of song that is sung on such occasions. A 49 is typically held in an isolated place and features drumming and singing.
 * 49th parallel between Canada and the US
 * Japanese GS1 country code
 * The number of the French department Maine-et-Loire
 * Since 4 BCE until 1993 AD, there have been 49 instances of a Master Number 22 year. The next Master Number 22 year will not be until 2299 AD.