198 (number)

← 197 198 199 →
← 190 191 192 193 194 195 196 197 198 199 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
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.

In mathematics

• 198 is the only number equal to the sum of its digits concatenated twice (198 = 11 + 99 + 88). ^{[1] [ self-published source? ]}
• 198 is the number of nonzero palindromes less than 10⁴. ^[2]
• 198 is the sum of products of terms in all partitions of the number 9. ^[3]
• 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. ^{[4] [5]}
• 198 is a companion Pell number. Its corresponding Pell number is 70. ^[6]
• 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. ^[7]
• 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. ^[4]
• 198 is a Harshad number, which means it is divisible by the sum of its digits. ^[8]
• 198 is both the average of a twin prime pair (197, 199), and the sum of 2 successive primes (97, 101). ^{[9] [10]}
• 198 is a coordination number for hexagonal lattices, which means it is the difference between two consecutive centered hexagonal numbers. ^[11] 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. ^[12]

In other fields

198 is also:

• The State Highway Police emergency telephone number in Brazil. ^{[13] [14]}

• The number of ridges on a U.S. dollar coin. ^[15]

See also

• The year AD 198 or 198 BC
• X-Men: The 198

References

1. "What's Special About This Number?". erich-friedman.github.io. Retrieved 2023-06-06.
2. "A050250 - OEIS". oeis.org. Retrieved 2023-06-05.
3. "A006906 - OEIS". oeis.org. Retrieved 2023-06-05.
4. America, Mathematical Association Of (2012-10-25). "NumberADay: 198". NumberADay. Retrieved 2023-06-04.
5. "A025366 - OEIS". oeis.org. Retrieved 2023-06-04.
6. "A002203 - OEIS". oeis.org. Retrieved 2023-06-04.
7. "A001078 - OEIS". oeis.org. Retrieved 2023-06-05.
8. "A005349 - OEIS". oeis.org. Retrieved 2023-06-04.
9. "A014574 - OEIS". oeis.org. Retrieved 2023-06-04.
10. "A000040 - OEIS". oeis.org. Retrieved 2023-06-04.
11. "A008458 - OEIS". oeis.org. Retrieved 2023-06-04.
12. "A005899 - OEIS". oeis.org. Retrieved 2023-06-05.
13. "Serviços de Utilidade Pública e de Emergência (SUP)". Agência Nacional de Telecomunicações (in Brazilian Portuguese). Retrieved 2023-06-04.
14. "Telefones Úteis". Secretaria da Segurança Pública (in Brazilian Portuguese). Retrieved 2023-06-04.
15. "Why Do Coins Have Ridges? | Mental Floss". 2022-08-18. Archived from the original on 2022-08-18. Retrieved 2022-08-24.