196 (number)

196 (one hundred [and] ninety-six) is the natural number following 195 and preceding 197.

← 195 196 197 →
Cardinalone hundred ninety-six
Ordinal196th
(one hundred ninety-sixth)
Factorization22 × 72
Divisors1, 2, 4, 7, 14, 28, 49, 98, 196
Greek numeralΡϞϚ´
Roman numeralCXCVI
Binary110001002
Ternary210213
Octal3048
Duodecimal14412
HexadecimalC416

In mathematicsEdit

196 is a square number, the square of 14. As the square of a Catalan number, it counts the number of walks of length 8 in the positive quadrant of the integer grid that start and end at the origin, moving diagonally at each step.[1] It is part of a sequence of square numbers beginning 0, 1, 4, 25, 196, ... in which each number is the smallest square that differs from the previous number by a triangular number.[2]

There are 196 one-sided heptominoes, the polyominoes made from 7 squares. Here, one-sided means that asymmetric polyominoes are considered to be distinct from their mirror images.[3]

A Lychrel number is a natural number which cannot form a palindromic number through the iterative process of repeatedly reversing its digits and adding the resulting numbers. 196 is the lowest number conjectured to be a Lychrel number in base 10; the process has been carried out for over a billion iterations without finding a palindrome, but no one has ever proven that it will never produce one.[4][5]

See alsoEdit

ReferencesEdit

  1. ^ Sloane, N. J. A. (ed.). "Sequence A001246 (Squares of Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A036449 (Values square, differences triangular)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A000988 (Number of one-sided polyominoes with n cells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A023108 (A023108)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Gabai, Hyman; Coogan, Daniel (1969). "On palindromes and palindromic primes". Mathematics Magazine. 42: 252–254. doi:10.2307/2688705. JSTOR 2688705. MR 0253979.