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{{Infobox number
| number = 49
| divisor = 1, 7, 49
}}
'''49''' ('''forty-nine''') is the [[Natural number|natural number]] following [[48 (number)|48]] and preceding [[50 (number)|50]].

==In mathematics==
'''Forty-nine''' is the square of the prime number [[7|seven]] and hence the fourth non-unitary square [[Prime number|prime]] of the form ''p''<sup>2</sup>

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).<ref>{{Cite web|url=https://oeis.org/A000931|title=Sloane's A000931 : Padovan sequence|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}}</ref>

Along with the number that immediately derives from it, 77, the only number under [[100 (number)|100]] not having its [[Home prime|home prime]] known ({{As of|2016|lc=y}}).

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

=== 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 {{sfrac|1|49}} is a repeating decimal with a period of 42:

:{{sfrac|1|49}} = {{overline|0.|0204081632 6530612244 8979591836 7346938775 51}} (42 digits repeat)

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|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 {{frac|1|49}} satisfies:
 
:<math>x = \frac{1}{50} + \frac{2x}{100} = \frac{1}{50}(1 + x)\, .</math>

==In chemistry==
* The [[Physics:Atomic number|atomic number]] of [[Chemistry:Indium|indium]].
* During the [[Physics:Manhattan Project|Manhattan Project]], [[Chemistry:Plutonium|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.<ref>
{{Cite journal|last=Hammel|first=E.F.|year=2000|title=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 
| journal = Los Alamos Science|volume=26|issue=1|pages=2–9|url=http://www.fas.org/sgp/othergov/doe/lanl/pubs/00818010.pdf}}</ref><ref>
{{Cite journal|last=Hecker|first=S.S.|year=2000|title=Plutonium: an historical overview. In: Challenges in Plutonium Science
| journal = Los Alamos Science|volume=26|issue=1|pages=1–2|url=http://www.fas.org/sgp/othergov/doe/lanl/pubs/number26.htm}}</ref>

==In astronomy==
* [[Astronomy:Messier object|Messier object]] [[Astronomy:Messier 49|M49]], a magnitude 10.0 [[Astronomy:Galaxy|galaxy]] in the [[Astronomy:Constellation|constellation]] [[Astronomy:Virgo (constellation)|Virgo]].
* The [[Astronomy:New General Catalogue|New General Catalogue]] object [[Astronomy:NGC 49|NGC 49]], a [[Spiral galaxy|spiral galaxy]] in the constellation [[Astronomy:Cetus|Cetus]].

==In religion==
* In [[Religion:Judaism|Judaism]]: the number of days of the Counting of the Omer and the number of years in a [[History:Jubilee (biblical)|Jubilee (biblical)]] cycle.
* The number of days and night [[Biography:Gautama Buddha|Siddhartha Gautama]] spent meditating as a holy man
* In [[Religion:Buddhism|Buddhism]], 49 days is one of the lengths of the intermediate state ([[Philosophy:Bardo|bardo]])

==In sports==
{{See also|49er (disambiguation)#Sports{{!}}49er § 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 [[Company:Manchester United F.C.|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.{{cn|date=May 2018}}
* 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==
{{see also|49er (disambiguation)#Music{{!}}49er § 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 [[Engineering:California Gold Rush|California Gold Rush]], recorded by Bob Dylan (on the album ''Self Portrait'') and by many others<ref>{{cite web| publisher=[[Organization:California State University, Fresno|California State University, Fresno]]| title=Days of Forty-Nine, The| url=https://www.fresnostate.edu/folklore/ballads/R198.html| accessdate=2022-10-09}}</ref><ref>{{cite web|
publisher=English Folk Dance and Song Society| title=RN2803: Days of '49| url=https://www.vwml.org/roudnumber/2803| accessdate=2022-10-09}}</ref>
* ''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.{{cn|date=May 2018}}

==In other fields==
{{Seealso|List of highways numbered 49}}
'''Forty-nine''' is:
* HP-49 series is a [[Company:Hewlett-Packard|Hewlett-Packard]] [[Engineering:Calculator|calculator]]
* ''49er'', one who participated in the 1849 [[Engineering:California Gold Rush|California Gold Rush]].
* The code for international direct dial phone calls to {{wipe|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.<ref>{{cite web|url=https://www.britannica.com/art/forty-nine-dance|title=Forty-nine dance|website=Encyclopedia Britannica|access-date=May 25, 2018}}</ref>
* 49th parallel between Canada and the US
* {{wipe|Japan}}ese [[Organization:GS1|GS1]] country code{{cn|date=May 2018}}
* The number of the French department Maine-et-Loire

==See also==
* List of highways numbered 49

==References==
<references/>


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[[Category:Integers]]

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