Strobogrammatic number
Encyclopedia
A strobogrammatic number is a number that, given a base and given a set of glyphs, appears the same whether viewed normally or upside down. In base 10, given a set of glyphs where 0, 1 and 8 are symmetrical around the horizontal axis, and 6 and 9 are the same as each other upside down (such as the digit characters in ASCII
using the font Stylus BT), the first few strobogrammatic numbers are:
0, 1, 8, 11, 69, 88, 96, 101, 111, 181, 609, 619, 689, 808, 818, 888, 906, 916, 986, 1001
1881 and 1961 were the most recent strobogrammatic years; the next strobogrammatic year will be 6009.
Although amateur aficionados of mathematics are quite interested in this concept, professional mathematicians generally are not. Like the concept of repunit
s and palindromic number
s, the concept of strobogrammatic numbers is base-dependent
. Unlike palindromicity it is also font dependent. But the concept of strobogrammatic numbers is not neatly expressible algebraically, the way that the concept of repunits is, or even the concept of palindromic numbers.
There are sets of glyphs for writing numbers in base 10, such as the Devanagari
and Gurmukhi of India
in which the numbers listed above are not strobogrammatic at all.
In binary, given a glyph for 1 consisting of a single line without hooks or serifs, all palindromic numbers are strobogrammatic, which means that all Mersenne numbers are strobogrammatic.
ASCII
The American Standard Code for Information Interchange is a character-encoding scheme based on the ordering of the English alphabet. ASCII codes represent text in computers, communications equipment, and other devices that use text...
using the font Stylus BT), the first few strobogrammatic numbers are:
0, 1, 8, 11, 69, 88, 96, 101, 111, 181, 609, 619, 689, 808, 818, 888, 906, 916, 986, 1001
1881 and 1961 were the most recent strobogrammatic years; the next strobogrammatic year will be 6009.
Although amateur aficionados of mathematics are quite interested in this concept, professional mathematicians generally are not. Like the concept of repunit
Repunit
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler...
s and palindromic number
Palindromic number
A palindromic number or numeral palindrome is a 'symmetrical' number like 16461, that remains the same when its digits are reversed. The term palindromic is derived from palindrome, which refers to a word like rotor that remains unchanged under reversal of its letters...
s, the concept of strobogrammatic numbers is base-dependent
Numeral system
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
. Unlike palindromicity it is also font dependent. But the concept of strobogrammatic numbers is not neatly expressible algebraically, the way that the concept of repunits is, or even the concept of palindromic numbers.
There are sets of glyphs for writing numbers in base 10, such as the Devanagari
Devanagari
Devanagari |deva]]" and "nāgarī" ), also called Nagari , is an abugida alphabet of India and Nepal...
and Gurmukhi of India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
in which the numbers listed above are not strobogrammatic at all.
In binary, given a glyph for 1 consisting of a single line without hooks or serifs, all palindromic numbers are strobogrammatic, which means that all Mersenne numbers are strobogrammatic.