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Tetradic Number


A tetradic (or four-way) number is a nonnegative integer that is a palindromic number in base 10 and has only 0, 1, and 8 as digits. The glyphs 0, 1, and 8 are assumed to be symmetric about both a horizontal and a vertical axis, with 1 written as a single stroke and 8 as a symmetric pair of loops. Under this convention, the numeral remains unchanged under horizontal or vertical reflection or a 180 degrees rotation. The first few tetradic numbers are 0, 1, 8, 11, 88, 101, 111, 181, 808, 818, ... (OEIS A006072).

The first few tetradic primes are 11, 101, 181, 18181, 1008001, 1180811, 1880881, 1881881, ... (OEIS A068188). The largest known tetradic prime number as of Apr. 2010 was

 10^(180054)+8R_(58567)·10^(60744)+1,

where R_n is a repunit. This number has 180055 decimal digits (PrimePages 2009).


See also

Dihedral Prime, Integer Sequence Primes, Palindromic Number

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References

PrimePages. "10^(180054)+8R(58567)10^(60744)+1." Sep. 8, 2009. https://t5k.org/primes/page.php?id=89907.Sloane, N. J. A. Sequences A006072/M4481 and A068188 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Tetradic Number

Cite this as:

Weisstein, Eric W. "Tetradic Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TetradicNumber.html

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