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{{Refimprove|date=May 2016}}
'''49''' is the ] following ] and preceding ].
{{Infobox number
| number = 49
| divisor = 1, 7, 49
}}
'''49''' ('''forty-nine''') is the ] following ] and preceding ].


==In mathematics==
<table border=1 style="float: right; border-collapse: collapse">
'''Forty-nine''' is the square of the prime number ] and hence the fourth non-unitary square ] of the form ''p''<sup>2</sup>.
<tr><td colspan=2 align=center>{{msg:numbers_40s}}
<tr><td>] <td>forty-nine
<tr><td>]<td>49th (forty-ninth)
<tr><td>]<td><math>49 = 7^2</math>
<tr><td>]<td>XLVIV
<tr><td>]<td>0110001
<tr><td>]<td>31
</table>


It appears in the ], 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 ] not having its ] known ({{As of|2016|lc=y}}).
'''Forty-nine''' is a ] based on 8.


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


49 is the smallest ] of a ].<ref>{{Cite OEIS |A006832 |Discriminants of totally real cubic fields. |access-date=2024-03-20 }}</ref>

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

The number of ] with 9 crossings is 49.<ref>{{cite OEIS|A002863|Number of prime knots with n crossings}}</ref>

=== 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 ====
{{See also| Repeating decimal}}

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 positive integers less than 49 and coprime to 49. (42 is the period.) Multiplying 020408163265306122448979591836734693877551 by each of these integers results in a ] 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 ] of ]. * The ] of ].
* During the ], ] 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>
* The span between ] as ordained in the ].
{{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
* The number of strings on a ] and the number of keys on a ].
| journal = ]|volume=26|issue=1|pages=2–9|url=http://www.fas.org/sgp/othergov/doe/lanl/pubs/00818010.pdf}}</ref><ref>
* The code for international direct dial phone calls to ].
{{Cite journal|last=Hecker|first=S.S.|year=2000|title=Plutonium: an historical overview. In: Challenges in Plutonium Science
* As in ''49er'', the moniker of those who participated in the 1849 gold rush.
| journal = Los Alamos Science|volume=26|issue=1|pages=1–2|url=http://www.fas.org/sgp/othergov/doe/lanl/pubs/number26.htm}}</ref>
* The years ], ] AD, or ].

==In astronomy==
* ] ], a ] 10.0 ] in the ] ].
* The ] object ], a ] in the constellation ].

==In religion==
* In ]: the number of days of the ] and the number of years in a ] cycle.
* The number of days and night ] spent meditating as a holy man
* In ], 49 days is one of the lengths of the intermediate state (])

==In sports==
{{See also|49er (disambiguation)#Sports{{!}}49er § Sports}}
* ''49er'', a member of the ] team of the ] (]).
* ] had a ] between May 2003 and October 2004 until they lost to ], which is a national record in ].
* ] ended his ] career as the only heavyweight champion with a perfect record—49 wins in 49 professional bouts, with 43 knockouts.{{cn|date=May 2018}}
* ] ] team ] 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 '']''
* "Days of '49", a 19th century folk song about the ], recorded by Bob Dylan (on the album '']'') and by many others<ref>{{cite web| publisher=]| title=Days of Forty-Nine, The| url=https://www.fresnostate.edu/folklore/ballads/R198.html| accessdate=2022-10-09}}</ref><ref>{{cite web|
publisher=]| title=RN2803: Days of '49| url=https://www.vwml.org/roudnumber/2803| accessdate=2022-10-09}}</ref>
* '']'' is a one-track solo album by ].
* In ] lore, it was at the junction of US Highway 49 and 61 in ], that legendary bluesman ] sold his soul to the devil in return for fame and success. In later years ] immortalized the road in the song "Highway 49", originally written by ].{{cn|date=May 2018}}

==In other fields==
{{Seealso|List of highways numbered 49}}
'''Forty-nine''' is:
* ] is a ] ]
* ''49er'', one who participated in the 1849 ].
* The ] phone calls to ]
* In the title of ]'s novel '']''
* In the title of the movies '']'' and '']''
* A 49 is a party after a ] 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=]|access-date=May 25, 2018}}</ref>
* ] between Canada and the US
* ]ese ] country code{{cn|date=May 2018}}
* The number of the French department ]
* 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.<ref>Sharp, Damian (2001). Simple Numerology: A Simple Wisdom book (A Simple Wisdom Book series). Red Wheel. p. 7. ISBN 978-1-57324-560-9.</ref>

==See also==
* ]

==References==
<references/>

{{Integers|zero}}


{{DEFAULTSORT:49 (Number)}}
]
] ]
]
]

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Find sources: "49" number – news · newspapers · books · scholar · JSTOR (May 2016) (Learn how and when to remove this message)
Natural number
← 48 49 50 →
← 40 41 42 43 44 45 46 47 48 49 → ← 0 10 20 30 40 50 60 70 80 90 →
Cardinalforty-nine
Ordinal49th
(forty-ninth)
Factorization7
Divisors1, 7, 49
Greek numeralΜΘ´
Roman numeralXLIX
Binary1100012
Ternary12113
Senary1216
Octal618
Duodecimal4112
Hexadecimal3116

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

In mathematics

Forty-nine is the square of the prime number seven and hence the fourth non-unitary square prime of the form p.

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 (as of 2016).

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

The number of prime knots with 9 crossings is 49.

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

See also: Repeating decimal

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

⁠1/49⁠ = 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 × 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...

because 1⁄49 satisfies:

x = 1 50 + 2 x 100 = 1 50 ( 1 + x ) . {\displaystyle 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

In religion

In sports

See also: 49er § Sports

In music

See also: 49er § Music

In other fields

See also: List of highways numbered 49

Forty-nine is:

See also

References

  1. "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  2. Sloane, N. J. A. (ed.). "Sequence A006832 (Discriminants of totally real cubic fields.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-20.
  3. Sloane, N. J. A. (ed.). "Sequence A002863 (Number of prime knots with n crossings)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. 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.
  5. Hecker, S.S. (2000). "Plutonium: an historical overview. In: Challenges in Plutonium Science". Los Alamos Science. 26 (1): 1–2.
  6. "Days of Forty-Nine, The". California State University, Fresno. Retrieved 2022-10-09.
  7. "RN2803: Days of '49". English Folk Dance and Song Society. Retrieved 2022-10-09.
  8. "Forty-nine dance". Encyclopedia Britannica. Retrieved May 25, 2018.
  9. Sharp, Damian (2001). Simple Numerology: A Simple Wisdom book (A Simple Wisdom Book series). Red Wheel. p. 7. ISBN 978-1-57324-560-9.
Integers
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