| ||||
|---|---|---|---|---|
| Cardinal | one hundred ninety-eight | |||
| Ordinal | 198th (one hundred ninety-eighth) | |||
| Factorization | 2 × 32 × 11 | |||
| Greek numeral | ΡϞΗ´ | |||
| Roman numeral | CXCVIII | |||
| Binary | 110001102 | |||
| Ternary | 211003 | |||
| Senary | 5306 | |||
| Octal | 3068 | |||
| Duodecimal | 14612 | |||
| Hexadecimal | C616 | |||
198 (one hundred [and] ninety-eight) is the natural number following 197 and preceding 199.
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Transcription
In mathematics
- 198 is the number of nonzero palindromes less than 104.[1]
- 198 is the sum of products of terms in all partitions of the number 9.[2]
- 198 is the smallest number that can be written as a sum of four positive squares in ten different ways: 198 = 12 + 22 + 72 + 122 = 12 + 42 + 92 + 102 = 22 + 32 + 42 + 132 = 22 + 32 + 82 + 112 = 22 + 52 + 52 + 122 = 22 + 72 + 82 + 92 = 32 + 32 + 62 + 122 = 32 + 52 + 82 + 102 = 42 + 52 + 62 + 112 = 62 + 72 + 72 + 82.[3][4]
- 198 is a companion Pell number. Its corresponding Pell number is 70.[5]
- 198 is the 4th term of the sequence a(n) = 10*a(n-1) - a(n-2) with a(0) = 0, a(1) = 2. This sequence has the property that for each n, if A = a(n), B = 2*a(n+1), C = 3*a(n+1) then A*B+1, A*C+1, B*C+1 are perfect squares.[6]
- 198 is the first number between a twin prime pair such that product of itself by its reversal (198 x 891 = 176418) is also between a twin prime pair.[3]
- 198 is a Harshad number, which means it is divisible by the sum of its digits.[7]
- 198 is both the average of a twin prime pair (197, 199), and the sum of 2 successive primes (97, 101).[8][9]
- 198 is a coordination number for hexagonal lattices, which means it is the difference between two consecutive centered hexagonal numbers.[10] In this case, 198 is the difference between 3367 and 3169 (34th and 33rd centered hexagonal numbers), so the hexagonal spatial arrangement of 3367 has 198 dots in the border.
- 198 is also the 8th coordination number for cubic lattices, making it the 6th number to be part of the coordination sequences for both cubic and hexagonal lattices.[11]
In other fields
198 is also:
- The State Highway Police emergency telephone number in Brazil.[12][13]
- The number of ridges on a U.S. dollar coin.[14]
See also
- The year AD 198 or 198 BC
- X-Men: The 198
References
- ^ "A050250 - OEIS". oeis.org. Retrieved 2023-06-05.
- ^ "A006906 - OEIS". oeis.org. Retrieved 2023-06-05.
- ^ a b America, Mathematical Association Of (2012-10-25). "NumberADay: 198". NumberADay. Retrieved 2023-06-04.
- ^ "A025366 - OEIS". oeis.org. Retrieved 2023-06-04.
- ^ "A002203 - OEIS". oeis.org. Retrieved 2023-06-04.
- ^ "A001078 - OEIS". oeis.org. Retrieved 2023-06-05.
- ^ "A005349 - OEIS". oeis.org. Retrieved 2023-06-04.
- ^ "A014574 - OEIS". oeis.org. Retrieved 2023-06-04.
- ^ "A000040 - OEIS". oeis.org. Retrieved 2023-06-04.
- ^ "A008458 - OEIS". oeis.org. Retrieved 2023-06-04.
- ^ "A005899 - OEIS". oeis.org. Retrieved 2023-06-05.
- ^ "Serviços de Utilidade Pública e de Emergência (SUP)". Agência Nacional de Telecomunicações (in Brazilian Portuguese). Retrieved 2023-06-04.
- ^ "Telefones Úteis". Secretaria da Segurança Pública (in Brazilian Portuguese). Retrieved 2023-06-04.
- ^ "Why Do Coins Have Ridges? | Mental Floss". 2022-08-18. Archived from the original on 2022-08-18. Retrieved 2022-08-24.
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