tetradic prime
(another Prime Pages' Glossary entries)
The Prime Glossary
Glossary: Prime Pages: Top 5000: Amateurs are often interested in numbers with special typographic qualities, such as the palindromes (which read the same forward and backward).  To define a vertical and horizontal analog of the palindromes, we first recognise, or pretend, that digits '0', '1', and '8' are each symmetric both horizontally and vertically, and the digits '6' and '9' are 180 degree rotations of each other.  With these assumptions, a tetradic (or 4-way) integer is a reflectable palindromic strobogrammatic integer that is the same in four ways; i.e., whether viewed from right to left, left to right, top to bottom, or upside down.  None of its digits can be other than '0,' '1,' or '8.'  The first few tetradic primes are 11, 101, 181, 18181, 1008001, and 1180811.

(Obviously tetradic primes could be generalized to any other radix, but even given the comment in the entry on strobogrammatic primes, this would be going too far.)

See Also: Palindrome, Strobogrammatic, TriadicPrime

References:

DO94
H. Dubner and R. Ondrejka, "A PRIMEr on palindromes," J. Recreational Math., 26:4 (1994) 256--267.
Ondrejka89
R. Ondrejka, "On tetradic or 4-way primes," J. Recreational Math., 21:1 (1989) 21-25.



Chris K. Caldwell © 1999-2014 (all rights reserved)