198 (one hundred [and] ninety-eight) is the natural number following 197 and preceding 199.

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

Wikimedia Commons has media related to 198 (number).