196 (number)
title: "196 (number)" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["arithmetic-dynamics", "integers"] topic_path: "general/arithmetic-dynamics" source: "https://en.wikipedia.org/wiki/196_(number)" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::data[format=table title="Infobox number"]
| Field | Value |
|---|---|
| number | 196 |
| divisor | 1, 2, 4, 7, 14, 28, 49, 98, 196 |
| :: |
| number = 196 | divisor= 1, 2, 4, 7, 14, 28, 49, 98, 196 196 (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. 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.
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.
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.{{cite journal | last1 = Gabai | first1 = Hyman | last2 = Coogan | first2 = Daniel | doi = 10.2307/2688705 | journal = Mathematics Magazine | jstor = 2688705 | mr = 253979 | pages = 252–254 | title = On palindromes and palindromic primes | volume = 42 | year = 1969| issue = 5
References
References
- {{cite OEIS. A001246. Squares of Catalan numbers
- {{cite OEIS. A036449. Values square, differences triangular
- {{cite OEIS. A000988. Number of one-sided polyominoes with n cells
- {{cite OEIS. A023108. A023108
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