Showing content from https://en.wikipedia.org/wiki/109_(number) below:
109 (number) - Wikipedia
From Wikipedia, the free encyclopedia
Natural number
109 (one hundred [and] nine) is the natural number following 108 and preceding 110.
109 is the 29th prime number. As 29 is itself prime, 109 is the tenth super-prime.[1] The previous prime is 107, making them both twin primes.[2]
109 is a centered triangular number.[3]
There are exactly:
- 109 different families of subsets of a three-element set whose union includes all three elements.[4]
- 109 different loops (invertible but not necessarily associative binary operations with an identity) on six elements.[5]
- 109 squares on an infinite chessboard that can be reached by a knight within three moves.[6]
There are 109 uniform edge-colorings to the 11 regular and semiregular (or Archimedean) tilings.[7]
The decimal expansion of 1/109 can be computed using the alternating series, with F ( n ) {\displaystyle F(n)} the n t h {\displaystyle n^{th}} Fibonacci number:
-
-
1 109 = ∑ n = 1 ∞ F ( n ) × 10 − ( n + 1 ) × ( − 1 ) n + 1 = 0.00917431 … {\displaystyle {\frac {1}{109}}=\sum _{n=1}^{\infty }{F(n)\times 10^{-(n+1)}}\times (-1)^{n+1}=0.00917431\dots }
The decimal expansion of 1/109 has 108 digits, making 109 a full reptend prime in decimal. The last six digits of the 108-digit cycle are 853211, the first six Fibonacci numbers in descending order.[8]
- ^ Sloane, N. J. A. (ed.). "Sequence A006450 (Primes with prime subscripts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006512 (Greater of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003465 (Number of ways to cover an n-set)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A057771 (Number of loops (quasigroups with an identity element) of order n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A018836 (Number of squares on infinite chess-board at ≤ n knight's moves from a fixed square)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Asaro, Laura; Hyde, John; et al. (January 2015). "Uniform edge-c-colorings of the Archimedean tilings". Discrete Mathematics. 338 (1): 19–22. doi:10.1016/j.disc.2014.08.015. Zbl 1308.52017.
- ^ "89, 109, and the Fibonacci Sequence". May 15, 2012. Retrieved November 8, 2022.
Integers −1 0s
100s
200s
300s
400s
500s
600s
700s
800s
900s
1000s
- 100,000
- 1,000,000
- 10,000,000
- 100,000,000
- 1,000,000,000
- 10,000,000,000
- 100,000,000,000
RetroSearch is an open source project built by @garambo
| Open a GitHub Issue
Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo
HTML:
3.2
| Encoding:
UTF-8
| Version:
0.7.4