49 (number)
Encyclopedia
49 is the natural number
following 48
and preceding 50
.
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).
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).
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:
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...
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
following 48
48 (number)
48 is the natural number following 47 and preceding 49. It is one third of a gross or four dozens.- In mathematics :Forty-eight is a double factorial of 6, a highly composite number. Like all other multiples of 6, it is a semiperfect number. 48 is the second 17-gonal number.48 is in abundance...
and preceding 50
50 (number)
This article discusses the number fifty. For the year 50 CE, see 50. For other uses of 50, see 50 50 is the natural number following 49 and preceding 51.-In mathematics:...
.
In mathematics
- Forty-nine is the square of seven and is therefore the fourth squared prime number.
The aliquot sum of forty-nine is 8. and this number has an aliquot sequence
Aliquot sequence
In mathematics, an aliquot sequence is a recursive sequence in which each term is the sum of the proper divisors of the previous term. The aliquot sequence starting with a positive integer k can be defined formally in terms of the sum-of-divisors function σ1 in the following way:For example, the...
of (8, 7, 1, 0 ).
49 is the 8th composite number
Composite number
A composite number is a positive integer which has a positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime 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
Padovan sequence
The Padovan sequence is the sequence of integers P defined by the initial valuesP=P=P=1,and the recurrence relationP=P+P.The first few values of P are...
, 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 3 digits not having its home prime
Home prime
In number theory, the home prime HP of an integer n greater than 1 is the prime obtained by repeatedly factoring the increasing concatenation of prime factors including repetitions. The mth intermediate stage in the process of determining HP is designated HPn...
known (as of late 2010).
Reciprocal
The fraction is a repeating decimal with a period of 42:- = 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
Cyclic permutation
A cyclic permutation or circular permutation is a permutation built from one or more sets of elements in cyclic order.The notion "cyclic permutation" is used in different, but related ways:- Definition 1 :right|mapping of 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 numberAtomic numberIn chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...
of indiumIndiumIndium is a chemical element with the symbol In and atomic number 49. This rare, very soft, malleable and easily fusible post-transition metal is chemically similar to gallium and thallium, and shows the intermediate properties between these two...
. - During the Manhattan ProjectManhattan ProjectThe Manhattan Project was a research and development program, led by the United States with participation from the United Kingdom and Canada, that produced the first atomic bomb during World War II. From 1942 to 1946, the project was under the direction of Major General Leslie Groves of the US Army...
, plutoniumPlutoniumPlutonium is a transuranic radioactive chemical element with the chemical symbol Pu and atomic number 94. It is an actinide metal of silvery-gray appearance that tarnishes when exposed to air, forming a dull coating when oxidized. The element normally exhibits six allotropes and four oxidation...
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 objectMessier objectThe Messier objects are a set of astronomical objects first listed by French astronomer Charles Messier in 1771. The original motivation of the catalogue was that Messier was a comet hunter, and was frustrated by objects which resembled but were not comets...
M49Messier 49Messier 49 is an elliptical / lenticular galaxy about 49 million light-years away in the constellation Virgo. The galaxy was discovered by Charles Messier in 1771.-Supernovae:...
, a magnitude 10.0 galaxyGalaxyA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
in the constellationConstellationIn modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
VirgoVirgo (constellation)Virgo is one of the constellations of the zodiac. Its name is Latin for virgin, and its symbol is . Lying between Leo to the west and Libra to the east, it is the second largest constellation in the sky...
. - The New General CatalogueNew General CatalogueThe New General Catalogue of Nebulae and Clusters of Stars is a well-known catalogue of deep sky objects in astronomy. It contains 7,840 objects, known as the NGC objects...
object NGC 49, a spiral galaxySpiral galaxyA spiral galaxy is a certain kind of galaxy originally described by Edwin Hubble in his 1936 work The Realm of the Nebulae and, as such, forms part of the Hubble sequence. Spiral galaxies consist of a flat, rotating disk containing stars, gas and dust, and a central concentration of stars known as...
in the constellation CetusCetusCetus is a constellation. Its name refers to Cetus, a sea monster in Greek mythology, although it is often called 'the whale' today. Cetus is located in the region of the sky that contains other water-related constellations such as Aquarius, Pisces, and Eridanus.-Ecliptic:Although Cetus is not...
. - The SarosSaros cycleThe saros is a period of 223 synodic months , that can be used to predict eclipses of the Sun and Moon. One saros after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, and a nearly identical eclipse will occur, in what is referred to as an eclipse cycle...
number of the solar eclipseSolar eclipseAs seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...
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 eclipseLunar eclipseA lunar eclipse occurs when the Moon passes behind the Earth so that the Earth blocks the Sun's rays from striking the Moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a...
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 calendarHebrew calendarThe Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
, the number of days of the Counting of the OmerCounting of the OmerCounting of the Omer is a verbal counting of each of the forty-nine days between the Jewish holidays of Passover and Shavuot... - The number of days and night Siddhartha GautamaGautama BuddhaSiddhārtha Gautama was a spiritual teacher from the Indian subcontinent, on whose teachings Buddhism was founded. In most Buddhist traditions, he is regarded as the Supreme Buddha Siddhārtha Gautama (Sanskrit: सिद्धार्थ गौतम; Pali: Siddhattha Gotama) was a spiritual teacher from the Indian...
spent meditating as a holy man - Surely We have created everything with fate. (Al-Qamar Surah, 49)
In sports
- See also 49er (disambiguation).
- 49er, the moniker of one who participated in the 1849 California Gold RushCalifornia Gold RushThe California Gold Rush began on January 24, 1848, when gold was found by James W. Marshall at Sutter's Mill in Coloma, California. The first to hear confirmed information of the gold rush were the people in Oregon, the Sandwich Islands , and Latin America, who were the first to start flocking to...
, as well as the NFL's San Francisco 49ersSan Francisco 49ersThe San Francisco 49ers are a professional American football team based in San Francisco, California, playing in the West Division of the National Football Conference in the National Football League . The team was founded in 1946 as a charter member of the All-America Football Conference and...
. - Houston AstrosHouston AstrosThe Houston Astros are a Major League Baseball team located in Houston, Texas. They are a member of the National League Central division. The Astros are expected to join the American League West division in 2013. Since , they have played their home games at Minute Maid Park, known as Enron Field...
Larry DierkerLarry DierkerLawrence Edward Dierker is a former Major League Baseball pitcher and manager. During a 14-year baseball career as a pitcher, he pitched from 1964–1977 for the Houston Colt .45s/Astros and the St. Louis Cardinals...
's retired uniform #49. - New York YankeesNew York YankeesThe New York Yankees are a professional baseball team based in the The Bronx, New York. They compete in Major League Baseball in the American League's East Division...
Ron GuidryRon GuidryRonald Ames Guidry , nicknamed "Louisiana Lightning" and "Gator", is a former Major League Baseball left-handed pitcher. He played his entire 14-year baseball career for the New York Yankees...
’s retired uniform #49. - ArsenalArsenal F.C.Arsenal Football Club is a professional English Premier League football club based in North London. One of the most successful clubs in English football, it has won 13 First Division and Premier League titles and 10 FA Cups...
had a 49 game unbeaten runThe Invincibles (football)In English football, "The Invincibles" has been used to refer to either the Preston North End team of the 1880s, or the Arsenal team of the 2003–04 season...
between May 2003 to October 2004 which is a national record in English footballFootball records in EnglandThis page details football records in England. Unless otherwise stated, records are taken from the Football League or Premier League. Where a different record exists for the top flight , this is also given.-League:Records in this section refer to The Football League and the Premier...
.
- 49er, the moniker of one who participated in the 1849 California Gold Rush
In music
- Funk #49, the title of a hit song by the James GangJames GangThe James Gang was a rock band formed in Cleveland, Ohio in 1966. Though the band was not a huge commercial success, except in the Northeast Ohio area, the fame garnered by guitarist Joe Walsh has since made the group more notable.- History :...
- Featured in the song title "49 Bye-Byes" in Crosby Stills and NashCrosby, Stills & Nash (and Young)Crosby, Stills & Nash is a folk rock supergroup made up of David Crosby, Stephen Stills and Graham Nash, also known as Crosby, Stills, Nash & Young when joined by occasional fourth member Neil Young...
's self-titled album - Song: 'Days of 49” by Bob DylanBob DylanBob Dylan is an American singer-songwriter, musician, poet, film director and painter. He has been a major and profoundly influential figure in popular music and culture for five decades. Much of his most celebrated work dates from the 1960s when he was an informal chronicler and a seemingly...
- 49:00... Of Your Time/Life49:00... Of Your Time/Life49:00 is the seventh official solo album by Paul Westerberg. The album was originally slated for a release on July 19, 2008 , but digital distribution problems delayed its release until July 21.The album is a single track that was sold on Amazon.com's Amazon MP3 service for 49 U.S. cents...
is a one-track solo album by Paul WesterbergPaul WesterbergPaul Westerberg is an American musician, best known as the former lead singer, rhythm guitarist, and songwriter of The Replacements, one of the seminal alternative rock bands of the 1980s. He launched a solo career after the dissolution of that band...
.
In other fields
Forty-nine is:- HP-49 seriesHP-49 seriesThe HP 49G series are Hewlett-Packard manufactured graphing calculators. They are the successors of the popular HP-48 series.There are four calculators in the 49 series of HP graphing calculators...
is a Hewlett Packard calculatorCalculatorAn electronic calculator is a small, portable, usually inexpensive electronic device used to perform the basic operations of arithmetic. Modern calculators are more portable than most computers, though most PDAs are comparable in size to handheld calculators.The first solid-state electronic... - I-49 is the designation for a USUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
interstate highway, currently open only in the state of LouisianaLouisianaLouisiana is a state located in the southern region of the United States of America. Its capital is Baton Rouge and largest city is New Orleans. Louisiana is the only state in the U.S. with political subdivisions termed parishes, which are local governments equivalent to counties...
, but planned to extend into ArkansasArkansasArkansas is a state located in the southern region of the United States. Its name is an Algonquian name of the Quapaw Indians. Arkansas shares borders with six states , and its eastern border is largely defined by the Mississippi River...
and MissouriMissouriMissouri is a US state located in the Midwestern United States, bordered by Iowa, Illinois, Kentucky, Tennessee, Arkansas, Oklahoma, Kansas and Nebraska. With a 2010 population of 5,988,927, Missouri is the 18th most populous state in the nation and the fifth most populous in the Midwest. It...
, eventually connecting Kansas CityKansas City, MissouriKansas City, Missouri is the largest city in the U.S. state of Missouri and is the anchor city of the Kansas City Metropolitan Area, the second largest metropolitan area in Missouri. It encompasses in parts of Jackson, Clay, Cass, and Platte counties...
and New Orleans - The code for international direct dial phone calls to GermanyGermanyGermany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
- In the title of Thomas PynchonThomas PynchonThomas Ruggles Pynchon, Jr. is an American novelist. For his most praised novel, Gravity's Rainbow, Pynchon received the National Book Award, and is regularly cited as a contender for the Nobel Prize in Literature...
's novel The Crying of Lot 49The Crying of Lot 49The Crying of Lot 49 is a novel by Thomas Pynchon, first published in 1966. The shortest of Pynchon's novels, it is about a woman, Oedipa Maas, possibly unearthing the centuries-old conflict between two mail distribution companies, Thurn und Taxis and the Trystero... - In the title of the movie Ladder 49Ladder 49Ladder 49 is a 2004 film about the heroics of a Baltimore fireman Jack Morrison, who is trapped inside a warehouse fire and his recollection of the events that got him to that point. The movie is a celebration of the firefighting profession and the life that comes with it...
- In the title of the movie 49 Up
- A 49 is a term used to describe a party after a powwowPowWowPowWow is a wireless sensor network mote developed by the Cairn team of IRISA/INRIA. The platform is currently based on IEEE 802.15.4 standard radio transceiver and on an MSP430 microprocessor...
or any gathering of American Indians, held by the participants. It also refers to a particular type of song that is sung on such occasions. A 49 is typically held in an isolated place and features drumming and singing. - 49th State of the USA: AlaskaAlaskaAlaska is the largest state in the United States by area. It is situated in the northwest extremity of the North American continent, with Canada to the east, the Arctic Ocean to the north, and the Pacific Ocean to the west and south, with Russia further west across the Bering Strait...
- 49th parallel49th parallel northThe 49th parallel north is a circle of latitude that is 49 degrees north of the Earth's equatorial plane. It crosses Europe, Asia, the Pacific Ocean, North America, and the Atlantic Ocean....
between Canada and the USA - Ernest HemingwayErnest HemingwayErnest Miller Hemingway was an American author and journalist. His economic and understated style had a strong influence on 20th-century fiction, while his life of adventure and his public image influenced later generations. Hemingway produced most of his work between the mid-1920s and the...
collection: The Fifth Column and The First Forty-Nine Stories - JapanJapanJapan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
ese GS1GS1Founded in 1977, GS1 is an international not-for-profit association dedicated to the development and implementation of global standards and solutions to improve the efficiency and visibility of supply and demand chains globally and across multiple sectors...
country code - The number of the French department Maine-et-LoireMaine-et-LoireMaine-et-Loire is a department in west-central France, in the Pays de la Loire region.- History :Maine-et-Loire is one of the original 83 departments created during the French Revolution on March 4, 1790. Originally it was called Mayenne-et-Loire, but its name was changed to Maine-et-Loire in 1791....