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== In mathematics == |
== In mathematics == |
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* Although composite, 145 is a [[Fermat pseudoprime]] |
* Although composite, 145 is a [[Fermat pseudoprime]] in [[16 (number)|sixteen]] bases with b < 145. In four of those bases, it is a [[strong pseudoprime]]: 1, 12, 17, and 144. |
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* the [[Mertens function]] returns [[0 (number)|0]].<ref>{{Cite web|url=https://oeis.org/A028442|title=Sloane's A028442 : Numbers n such that Mertens' function is zero|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}</ref> |
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* 145 is a [[pentagonal number]]<ref>{{Cite web|url=https://oeis.org/A000326|title=Sloane's A000326 : Pentagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}</ref> and a [[centered square number]].<ref>{{Cite web|url=https://oeis.org/A001844|title=Sloane's A001844 : Centered square numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}</ref> |
* 145 is a [[pentagonal number]]<ref>{{Cite web|url=https://oeis.org/A000326|title=Sloane's A000326 : Pentagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}</ref> and a [[centered square number]].<ref>{{Cite web|url=https://oeis.org/A001844|title=Sloane's A001844 : Centered square numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}</ref> |
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* <math>145 = 12^2 + 1^2 = 8^2 + 9^2</math>. 145 is the fourth number that is the sum of two different pairs of [[square (algebra)|squares]]. Also, 145 is the result of 3<sup>4</sup> + 4<sup>3</sup>, making it a [[Leyland number]]. |
* <math>145 = 12^2 + 1^2 = 8^2 + 9^2</math>. 145 is the fourth number that is the sum of two different pairs of [[square (algebra)|squares]]. Also, 145 is the result of 3<sup>4</sup> + 4<sup>3</sup>, making it a [[Leyland number]]. |
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* <math>145 = 1! + 4! + 5!</math>, making it a [[factorion]].<ref name=":0">{{Cite web|url=https://oeis.org/A014080|title=Sloane's A014080 : Factorions|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}</ref> The only other numbers that have |
* <math>145 = 1! + 4! + 5!</math>, making it a [[factorion]].<ref name=":0">{{Cite web|url=https://oeis.org/A014080|title=Sloane's A014080 : Factorions|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}</ref> The only other numbers that have this property are [[1 (number)|1]], [[2 (number)|2]] and [[40,000|40585]].<ref name=":0" /> |
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* <math>145=5^2+5!=11^2+4!=12^2+1!</math>, making 145 the smallest number that can be written as the sum of a |
* <math>145=5^2+5!=11^2+4!=12^2+1!</math>, making 145 the smallest number that can be written as the sum of a [[Square number|square]] number and a factorial in 3 ways. The next number with this property is [[40,000|46249]].<ref>{{Cite web |title=A359013 - OEIS |url=https://oeis.org/A359013 |access-date=2022-12-11 |website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation}}</ref> |
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==In the military== |
==In the military== |
Latest revision as of 20:17, 5 March 2024
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Cardinal | one hundred forty-five | |||
Ordinal | 145th (one hundred forty-fifth) | |||
Factorization | 5 × 29 | |||
Divisors | 1, 5, 29, 145 | |||
Greek numeral | ΡΜΕ´ | |||
Roman numeral | CXLV | |||
Binary | 100100012 | |||
Ternary | 121013 | |||
Senary | 4016 | |||
Octal | 2218 | |||
Duodecimal | 10112 | |||
Hexadecimal | 9116 |
145 (one hundred [and] forty-five) is the natural number following 144 and preceding 146.
In mathematics
[edit]- Although composite, 145 is a Fermat pseudoprime in sixteen bases with b < 145. In four of those bases, it is a strong pseudoprime: 1, 12, 17, and 144.
- the Mertens function returns 0.[1]
- 145 is a pentagonal number[2] and a centered square number.[3]
- . 145 is the fourth number that is the sum of two different pairs of squares. Also, 145 is the result of 34 + 43, making it a Leyland number.
- , making it a factorion.[4] The only other numbers that have this property are 1, 2 and 40585.[4]
- , making 145 the smallest number that can be written as the sum of a square number and a factorial in 3 ways. The next number with this property is 46249.[5]
In the military
[edit]- USS Armada (AM-145) was a United States Navy Admirable-class minesweeper during World War II
- USS Colbert (APA-145) was a United States Navy Haskell-class attack transport during World War II
- USS General Harry Taylor (AP-145) was a United States Navy General G. O. Squier-class transport during World War II
- USS Greer (DD-145) was a United States Navy Wickes-class destroyer during World War II
- USS Huse (DE-145) was a United States Navy Edsall-class destroyer escort during World War II
- USS Roanoke (CL-145) was a United States Navy Worcester-class cruiser following World War II
In sports
[edit]- The Grand Union Canal Race is a 145-mile ultramarathon from Birmingham to London along the Grand Union Canal
In transportation
[edit]- Eurocopter EC 145 is a twin-engine light utility helicopter
- The Delahaye 145 Sports Car from 1938[6]
- The Alfa Romeo 145 car produced between 1994 and 2001
- Volvo 145 Express station wagon
- ERJ 145 regional jets produced by Embraer
- Golden Gate Transit Bus Route 145[7]
- London Bus Route 145[8]
In other fields
[edit]145 is also:
- The year AD 145 or 145 BC
- 145 AH is a year in the Islamic calendar that corresponds to 762 – 763 CE
- 145 Adeona is a large main belt asteroid
- Psalm 145
- Sonnet 145
- Apple Computer laptops, such as the PowerBook 145 and PowerBook 145B
- Puff Daddy song “Picture it” includes the lyrics “in something foreign soarin’ 145”
- Tsuu T'ina Nation 145 Indian reserve in Alberta, Canada
- 145 mg medicine tablets, as with Tricor
- "One Four Five" is a song by The Cat Empire
See also
[edit]- List of highways numbered 145
- United Nations Security Council Resolution 145
- United States Supreme Court cases, Volume 145
References
[edit]- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 140
- ^ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
- ^ "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
- ^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
- ^ a b "Sloane's A014080 : Factorions". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
- ^ "A359013 - OEIS". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-11.
- ^ "1938 Delahaye 145 le mans Slot Car 1/32". www.tertrerouge-racingcars.com. Archived from the original on 16 September 2008. Retrieved 14 January 2022.
- ^ "Ferry Schedules & Maps - Ferry | Golden Gate".
- ^ "Route 145". London Bus Routes.
External links
[edit]![](http://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png)
Wikimedia Commons has media related to 145 (number).
- The Natural Number 145
- Parker, Matt. "145 and the Melancoil". Numberphile. Brady Haran. Archived from the original on 2013-05-14. Retrieved 2013-04-06.