223 (number): Difference between revisions
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== In mathematics == |
== In mathematics == |
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223 is: |
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*a [[prime number]],<ref>{{Cite OEIS|A000040|The prime numbers}}</ref> |
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*a [[lucky prime]],<ref>{{Cite OEIS|A031157|Numbers that are both lucky and prime}}</ref> |
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*a left-[[truncatable prime]],<ref>{{Cite OEIS|A024770|Right-truncatable primes: every prefix is prime}}</ref>, and a [[Truncatable prime#Decimal truncatable primes|left-and-right-truncatable prime]].<ref>{{Cite OEIS|A077390|Primes which leave primes at every step if most significant digit and least significant digit are deleted until a one digit or two digit prime is obtained}}</ref> |
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| ⚫ | Among the 720 [[permutation]]s of the numbers from 1 to 6, exactly 223 of them have the property that at least one of the numbers is fixed in place by the permutation and the numbers less than it and greater than it are separately permuted among themselves.<ref>{{Cite OEIS|A006932|Number of permutations of [n] with at least one strong fixed point}}</ref> |
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In connection with [[Waring's problem]], 223 requires the maximum number of terms (37 terms) when expressed as a sum of positive fifth powers, and is the only number that requires that many terms.<ref>{{Cite OEIS|A048267| |
In connection with [[Waring's problem]], 223 requires the maximum number of terms (37 terms) when expressed as a sum of positive fifth powers, and is the only number that requires that many terms.<ref>{{Cite OEIS|A048267|2=Largest integer requiring n fifth powers to sum to it, starting with n=28}}</ref> |
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==In other fields== |
==In other fields== |
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Latest revision as of 12:44, 5 July 2024
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|---|---|---|---|---|
| Cardinal | two hundred twenty-three | |||
| Ordinal | 223rd (two hundred twenty-third) | |||
| Factorization | prime | |||
| Prime | 48th | |||
| Greek numeral | ΣΚΓ´ | |||
| Roman numeral | CCXXIII | |||
| Binary | 110111112 | |||
| Ternary | 220213 | |||
| Senary | 10116 | |||
| Octal | 3378 | |||
| Duodecimal | 16712 | |||
| Hexadecimal | DF16 | |||
223 (two hundred [and] twenty-three) is the natural number following 222 and preceding 224.
In mathematics[edit]
223 is:
- a prime number,[1]
- a lucky prime,[2]
- a left-truncatable prime,[3], and a left-and-right-truncatable prime.[4]
Among the 720 permutations of the numbers from 1 to 6, exactly 223 of them have the property that at least one of the numbers is fixed in place by the permutation and the numbers less than it and greater than it are separately permuted among themselves.[5]
In connection with Waring's problem, 223 requires the maximum number of terms (37 terms) when expressed as a sum of positive fifth powers, and is the only number that requires that many terms.[6]
In other fields[edit]
- .223 (disambiguation), the caliber of several firearm cartridges
- The years 223 and 223 BC
- The number of synodic months of a Saros
References[edit]
- ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A024770 (Right-truncatable primes: every prefix is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A077390 (Primes which leave primes at every step if most significant digit and least significant digit are deleted until a one digit or two digit prime is obtained)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006932 (Number of permutations of [n] with at least one strong fixed point)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A048267 (Largest integer requiring n fifth powers to sum to it, starting with n=28)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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