198 (number)

From HandWiki

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