Tetradic number

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A tetradicnumber, also known as a four-waynumber, is a number that remains the same when flipped back to front, flipped front to back, mirrored up-down, or flipped up-down. The only numbers that remain the same which turned up-side-down or mirrored are 0, 1, and 8, so a tetradic number is a palindromic number containing only 0, 1, and 8 as digits. (This is dependent on the use of a handwriting style or font in which these digits are symmetrical, as well on the use of Arabic numerals in the first place.) The first few tetradic numbers are 1, 8, 11, 88, 101, 111, 181, 808, 818, ... (OEIS A006072). [1] [2] [3] [4]

Tetradic numbers are also known as four-way numbers due to the fact that they have four-way symmetry and can flipped back to front, flipped front to back, mirrored up-down, or flipped up-down and always stay the same. The four-way symmetry explains the name, due to tetra- being the Greek prefix for four. Tetradic numbers are both strobogrammatic and palindromic. [3] [4]

A larger tetradic number can always be generated by adding another tetradic number to each end, retaining the symmetry.

Tetradic primes

Tetradic primes are a specific type of tetradic number defined as tetradic numbers that are also prime numbers. The first few tetradic primes are 11, 101, 181, 18181, 1008001, 1180811, 1880881, 1881881, ... (OEIS A068188). [5] [6] [7] [8] [9] [10]

The largest known tetradic prime as of April 2010 is

where is a repunit, that is, a number which contains only the digit 1 repeated times. The prime has 180,055 decimal digits. [3]

Related Research Articles

A palindromic number is a number that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term palindromic is derived from palindrome, which refers to a word whose spelling is unchanged when its letters are reversed. The first 30 palindromic numbers are:

11 (eleven) is the natural number following 10 and preceding 12. It is the first repdigit. In English, it is the smallest positive integer whose name has three syllables.

89 (eighty-nine) is the natural number following 88 and preceding 90.

73 (seventy-three) is the natural number following 72 and preceding 74. In English, it is the smallest natural number with twelve letters in its spelled out name.

101 is the natural number following 100 and preceding 102.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

900 is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10 it is a Harshad number. It is also the first number to be the square of a sphenic number.

2000 is a natural number following 1999 and preceding 2001.

10,000 is the natural number following 9,999 and preceding 10,001.

196 is the natural number following 195 and preceding 197.

<span class="mw-page-title-main">1,000,000</span> Natural number

One million (1,000,000), or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian millione, from mille, "thousand", plus the augmentative suffix -one.

100,000,000 is the natural number following 99,999,999 and preceding 100,000,001.

In mathematics, a pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once. For example, 1234567890 is a pandigital number in base 10. The first few pandigital base 10 numbers are given by :

288 is the natural number following 287 and preceding 289. Because 288 = 2 · 12 · 12, it may also be called "two gross" or "two dozen dozen".

20,000 is the natural number that comes after 19,999 and before 20,001.

60,000 (sixty thousand) is the natural number that comes after 59,999 and before 60,001. It is a round number. It is the value of (F25).

262 is a natural number proceeded by the number 261 and followed by 263. It has the prime factorization 2·131.

References

  1. ↑ Sloane, N. J. A. Sequences A006072/M4481 in "The On-Line Encyclopedia of Integer Sequences."
  2. ↑ Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics (2nd ed.). CRC Press. ISBN   978-1420035223.
  3. 1 2 3 "Tetradic Number". Wolfram MathWorld. Retrieved October 28, 2018.
  4. 1 2 "tetradic number". Everthing2. January 5, 2002. Retrieved October 28, 2018.
  5. ↑ Sloane, N. J. A. Sequences A068188 in "The On-Line Encyclopedia of Integer Sequences."
  6. ↑ Caldwell, Chris K. "tetradic prime". The Prime Glossary. The University of Tennessee Martin. Retrieved October 28, 2018.
  7. ↑ H. Dubner and R. Ondrejka , "A PRIMEr on palindromes," J. Recreational Math., 26:4 (1994) 256–267.
  8. ↑ R. Ondrejka, "On tetradic or 4-way primes," J. Recreational Math., 21:1 (1989) 21–25.
  9. ↑ Ondrejka, R. "The Top Ten Prime Numbers" (PDF). The Prime Pages. Retrieved October 28, 2018.
  10. ↑ Carmody, Phil. "Totally Tetradic!". Fat Phil. Retrieved October 28, 2018.
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