Octodecimal

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Octodecimal refers to counting based on the number eighteen, and its digits may be the numbers 0~9 and the letters A~H. Like duodecimal, an octodecimal multiplication table has more regularity than a decimal one, because similar as 12, 18 is also an abundant number and the numbers below or above it are primes. Having the same prime factors as six and twelve (2 and 3), the inverse of any 3-smooth number has a terminating representation likewise in octodecimal as in senary and duodecimal. Which factor can be squared and still be a divisor is where it differs: duodecimal squares 2 while octodecimal squares 3.

Certain powers of 7 are palindromes in octodecimal: 73 = 111, 74 = 777, 76 = 12321, and 79 = 1367631.

After 11 (the decimal number 19), the next 25000 octodecimal repunits are all composite. In fact, the next octodecimal repunit prime after 11 contains 25667 1s, and it is only probable prime. Thus, no proved octodecimal repunit prime after 11.

The Ndom language of Papua New Guinea, which employs senary counting, includes a basic word for 18 and another for 36. The Mayan Long Count calendar employs a "modified vigesimal" counting system that sets apart 360 as the number of days in a year, i.e. 18 months with 20 days.

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