Encyclopedia
Dodecagonal number
Figurate number representing a dodecagon
In mathematics, a dodecagonal number is a figurate number that represents a dodecagon. The dodecagonal number for n is given by the formula
The first few dodecagonal numbers are:
01Properties
- The dodecagonal number for n can be calculated by adding the square of n to four times the (n - 1)th pronic number, or to put it algebraically,
.
- Dodecagonal numbers consistently alternate parity, and in base 10, their units place digits follow the pattern 1, 2, 3, 4, 5, 6, 7, 8, 9, 0.
- By the Fermat polygonal number theorem, every number is the sum of at most 12 dodecagonal numbers.
is the sum of the first n natural numbers congruent to 1 mod 10.
is the sum of all odd numbers from 4n+1 to 6n+1.
02Sum of reciprocals
A formula for the sum of the reciprocals of the dodecagonal numbers is given by
Sources and credits
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