118 (number): Difference between revisions
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==In mathematics== |
==In mathematics== |
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There is no answer to the equation [[Euler's totient function|φ]](''x'') = 118, making 118 a [[nontotient]]. |
There is no answer to the equation [[Euler's totient function|φ]](''x'') = 118, making 118 a [[nontotient]].<ref>{{cite OEIS|A005277|Nontotients}}</ref> |
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118 is the smallest ''n'' such that the range ''n'', ''n'' + 1, ... 4''n''/3 contains at least one prime from each of these forms: 4''x'' + 1, 4''x'' - 1, 6''x'' + 1 and 6''x'' - 1. |
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Four expressions for 118 as the sum of three positive integers have the same product: |
Four expressions for 118 as the sum of three positive integers have the same product: |
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118 is the smallest number that can be expressed as four sums with the same product in this way.<ref>Wells, D. ''[[The Penguin Dictionary of Curious and Interesting Numbers]]'' London: Penguin Group. (1987): 134 - 135</ref> |
118 is the smallest number that can be expressed as four sums with the same product in this way.<ref>Wells, D. ''[[The Penguin Dictionary of Curious and Interesting Numbers]]'' London: Penguin Group. (1987): 134 - 135</ref> |
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118 is a [[Leyland number#Leyland_number_of_the_second_kind|Leyland number of the second kind]]. |
Because of its expression as {{nowrap|1=118 = 3<sup>5</sup> − 5<sup>3</sup>}}, it is a [[Leyland number#Leyland_number_of_the_second_kind|Leyland number of the second kind]].<ref>{{cite OEIS|A045575|Nonnegative numbers of the form x^y - y^x, for x,y > 1}}</ref> |
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==In telephony== |
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* The beginning of [[Directory assistance|directory enquiries]] numbers in the United Kingdom,<ref>[http://www.telecom-tariffs.co.uk/dialdirq.htm List of UK 118 directory enquiry services]</ref> [[France]], [[Germany]], [[Greece]], [[Latvia]], [[118 118 (Sweden)|Sweden]], [[Ireland]], [[Iran]] and [[Türk Telekom|Turkey]] |
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* The [[Japan Coast Guard|emergency at sea]] [[emergency telephone number]] in [[Japan]]<!-- in case you need a reference: http://tools.ietf.org/html/draft-arai-ecrit-japan-req-00 --> |
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* The [[fire]] [[emergency telephone number]] in [[Switzerland]] and [[Maldives]] |
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* The [[medical]] [[emergency telephone number]] in [[Bolivia]] and [[Indonesia]] |
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* The [[emergency medical services in Italy]] |
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==In other fields== |
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'''One hundred and eighteen''' is also: |
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* [[Oganesson]], an element with atomic number 118 |
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* ''[[118 (TV series)|118]]'', a 255-episode Singaporean television drama airing from 2014 to 2015 |
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* The number of elements in the [[Periodic Table]]. |
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*The 118th Tactical Fighter Squadron "Mobius", a fictional fighter squadron in ''[[Ace Combat 04: Shattered Skies]]'' |
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==In dates== |
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* 1/18 can also represent the day January 18. The 118th day of the year is April 28, on regular years. On leap years it is April 27. |
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==See also== |
==See also== |
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* [[118 (disambiguation)]] |
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* [[List of highways numbered 118]] |
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* [[118 118 (disambiguation)|118 118 European directory enquiries]] |
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* [[118th Street (Manhattan)|118th Street, Manhattan]] |
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==References== |
==References== |
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Revision as of 07:41, 14 August 2022
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|---|---|---|---|---|
| Cardinal | one hundred eighteen | |||
| Ordinal | 118th (one hundred eighteenth) | |||
| Factorization | 2 × 59 | |||
| Divisors | 1, 2, 59, 118 | |||
| Greek numeral | ΡΙΗ´ | |||
| Roman numeral | CXVIII | |||
| Binary | 11101102 | |||
| Ternary | 111013 | |||
| Senary | 3146 | |||
| Octal | 1668 | |||
| Duodecimal | 9A12 | |||
| Hexadecimal | 7616 | |||
118 (one hundred [and] eighteen) is the natural number following 117 and preceding 119.
In mathematics
There is no answer to the equation φ(x) = 118, making 118 a nontotient.[1]
Four expressions for 118 as the sum of three positive integers have the same product:
- 14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72 = 118 and
- 14 × 50 × 54 = 15 × 40 × 63 = 18 × 30 × 70 = 21 × 25 × 72 = 37800.
118 is the smallest number that can be expressed as four sums with the same product in this way.[2]
Because of its expression as 118 = 35 − 53, it is a Leyland number of the second kind.[3]
118!! - 1 is a prime number, where !! denotes the double factorial (the product of even integers up to 118).[4]
See also
References
Wikimedia Commons has media related to 118 (number).
- ^ Sloane, N. J. A. (ed.). "Sequence A005277 (Nontotients)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134 - 135
- ^ Sloane, N. J. A. (ed.). "Sequence A045575 (Nonnegative numbers of the form x^y - y^x, for x,y > 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007749 (Numbers k such that k!! - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.