What is the meaning of Palindrome in English?
noun:
Origin:
early 17th century: from Greek palindromos ‘running back again’, from palin ‘again’ + drom- (from dramein ‘to run’).
Translate Palindrome to
- 1. প্যালিনড্রোম
👉What are palindromic numbers?
Palindromic numbers are numbers that read the same forwards and backward, like 121, 33, or 9009, exhibiting symmetry in their digits. This property applies to single digits (0-9) and multi-digit numbers, with examples including 11, 272, 101, and 161161. The concept originates from the Greek "palindromos," meaning "running back again," and applies to words and sentences too, but for numbers, it's about digit reversal. [1, 2, 3, 4]
Examples of Palindromic Numbers
- Single-digit: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
- Two-digit: 11, 22, 33, ... 99
- Three-digit: 101, 121, 232, 303, ...
- Four-digit: 1001, 1221, 8008, 9999 [1, 2, 4]
Key Characteristics
- Mirror Symmetry: The first half of the digits determines the second half due to reflection.
- Base-Dependent: A number's palindromic nature can depend on the number base (though typically base-10 is assumed). [1, 2]
Palindromic Properties
- Even vs. Odd Digits: Palindromes with an even number of digits have a different count pattern than those with an odd number of digits.
- Divisibility: Some patterns emerge; for instance, all 4-digit palindromes (like ) are divisible by 11, as simplifies to , both divisible by 11. [2, 5, 6, 7, 8]
Related Concepts
- Lychrel Numbers: Numbers that are suspected never to form a palindrome through the "reverse-and-add" process, like 196.
- Palindromic-Type Numbers: Numbers that become palindromes after specific mathematical operations, such as 1825 + 5281 = 7106 (not a palindrome), but related patterns exist. [5, 9, 10]
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