A tetradic number
is one which is both strobogrammatic
in nature. Thus it is the same when viewed from left to right
, right to left
, top to bottom
or upside down
. This four-way symmetry
explains the name, tetra-
being the greek prefix for four.
The only digits that can be found in a tetradic number are 0, 1 and 8, since although matched pairs of 6 and 9 can be used in strobogrammatic numbers, they won't yield a palindrome. Thus the first few tetradic numbers are 0,1,8,11,88,101.... (sequence A006072 in the Online Encyclopedia of Integer Sequences).
Given a tetradic number, a larger one can always be generated by adding another tetradic number to each end, retaining the symmetry.
There are tetradic primes, the first half dozen being 11, 101, 181, 18181, 1008001, and 1180811. The largest found as of April, 2004 appears to be one of 51001 digits, beating a previous record of 30803 digits, but it contains only 1's and 0's. If you'd like some 8's as well, try the 15601 digit number obtained by writing 1560 copies of 1808010808 and tagging a 1 on the end. See http://listserv.nodak.edu/scripts/wa.exe?A2=ind0404&L=nmbrthry&F=&S=&P=1774 and http://listserv.nodak.edu/scripts/wa.exe?A2=ind0202&L=nmbrthry&F=&S=&P=1065 for more info on these and other types of large palindrome-based primes.