196 (number)
| ||||
|---|---|---|---|---|
| Cardinal | one hundred ninety-six | |||
| Ordinal | 196th (one hundred ninety-sixth) | |||
| Factorization | 22 × 72 | |||
| Divisors | 1, 2, 4, 7, 14, 28, 49, 98, 196 | |||
| Greek numeral | ΡϞϚ´ | |||
| Roman numeral | CXCVI | |||
| Binary | 110001002 | |||
| Ternary | 210213 | |||
| Senary | 5246 | |||
| Octal | 3048 | |||
| Duodecimal | 14412 | |||
| Hexadecimal | C416 | |||
196 (one hundred [and] ninety-six) is the natural number following 195 and preceding 197.
In mathematics
[edit]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 smallest 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 also
[edit]References
[edit]- ^ Sloane, N. J. A. (ed.). "Sequence A001246 (Squares of Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A036449 (Values square, differences triangular)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000988 (Number of one-sided polyominoes with n cells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A023108 (A023108)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Gabai, Hyman; Coogan, Daniel (1969). "On palindromes and palindromic primes". Mathematics Magazine. 42 (5): 252–254. doi:10.2307/2688705. JSTOR 2688705. MR 0253979.
