196 (number)

Short description: Natural number

| <- 195  | 196 |  197 ->

|
|

← 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-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
Quaternary| 30104
Quinary| 12415
Senary| 5246
Octal| 3048
Duodecimal| 14412
Hexadecimal| C416
Vigesimal| 9G20
Base 36| 5G36

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

## In mathematics

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

* 196 (disambiguation)

## References

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

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/196 (number). Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=196_(number)&oldid=294138"