49 (number)

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

In mathematics

• Forty-nine is the square of seven

The aliquot sum of forty-nine is 8, and this number has an aliquot sequence of (8, 7, 1, 0).

49 is the 8th composite number in the 7-aliquot tree.

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.

It appears in the Padovan sequence, preceded by the terms 21, 28, 37 (it is the sum of the first two of these).^[1]

Along with the number that immediately derives from it, 77, the only number under 3 digits not having its home prime known (as of late 2010).

Reciprocal

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

 ¹⁄₄₉ = 0.0204081632 6530612244 8979591836 7346938775 51 (42 repeating digits)

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

• 020408163265306122448979591836734693877551 × 2 = 040816326530612244897959183673469387755102
• 020408163265306122448979591836734693877551 × 3 = 061224489795918367346938775510204081632653
• 020408163265306122448979591836734693877551 × 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...

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.^[2][3]

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.
• The Saros number of the solar eclipse series which began on -1248 February 22 and ended on 32 March. The duration of Saros series 49 was 1280.1 years, and it contained 72 solar eclipses.
• The Saros number of the lunar eclipse series which began on -1217 June 21 and ended on 81 August. The duration of Saros series 49 was 1298.1 years, and it contained 73 lunar eclipses.

In religion

• On the Hebrew calendar, the number of days of the Counting of the Omer
• 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

See also 49er.

• 49er, the moniker of one who participated in the 1849 California Gold Rush, as well as the NFL's San Francisco 49ers.
• Houston Astros Larry Dierker's retired uniform #49.
• New York Yankees Ron Guidry’s retired uniform #49.
• Arsenal had a 49 game unbeaten run between May 2003 to October 2004 until they lost to Manchester United which is a national record in English football.

In music

• Featured in the song title "49 Bye-Byes" in Crosby Stills and Nash's self-titled album
• "Days of 49", a Bob Dylan song
• 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: “Long tall momma / She don’t pay me no mind / All she wanna do / Walk the Highway 49.”

In other fields

Forty-nine is:

• HP-49 series is a Hewlett Packard calculator
• Interstate 49 is the designation for a US interstate highway, currently open only in the state of Louisiana, but planned to extend into Arkansas and Missouri, eventually connecting Kansas City and New Orleans
• CA-49, a California highway that connects many of the Gold Rush towns in the Sierra Nevada foothills.
• 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 movie Ladder 49
• In the title of the movie 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.^[4]
• 49th State of the USA: Alaska
• 49th parallel between Canada and the USA
• Ernest Hemingway collection: The Fifth Column and The First Forty-Nine Stories
• Japanese GS1 country code
• The number of the French department Maine-et-Loire

References

1. ↑ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
2. ↑ Hammel, E.F. (2000). "The taming of "49" — Big Science in little time. Recollections of Edward F. Hammel, pp. 2-9. In: Cooper N.G. Ed. (2000). Challenges in Plutonium Science" (PDF). Los Alamos Science. 26 (1): 2–9. 
3. ↑ Hecker, S.S. (2000). "Plutonium: an historical overview. In: Challenges in Plutonium Science". Los Alamos Science. 26 (1): 1–2. 
4. ↑ Audio commentary by Sherman Aexie and Sean Axmaker on the DVD of The Exiles