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Because of the tremendous diversity allowed, in combination, by the valences of common atoms and their ability to form rings, the number of possible cyclic structures, even of small size (e.g., < 17 total atoms) numbers in the many billions. Cyclic compound examples: All-carbon (carbocyclic) and more complex natural cyclic compounds
Since the compounds are composed only of carbon atoms, they are allotropes of carbon. Possible bonding patterns include all double bonds (a cyclic cumulene) or alternating single bonds and triple bonds (a cyclic polyyne). [1] [2] [3] The first cyclocarbon synthesized is cyclo[18]carbon (C 18). [4]
A homocycle or homocyclic ring is a ring in which all atoms are of the same chemical element. [1] A heterocycle or heterocyclic ring is a ring containing atoms of at least two different elements, i.e. a non-homocyclic ring. [2] A carbocycle or carbocyclic ring is a homocyclic ring in which all of the atoms are carbon. [3]
where b is the number base (10 for decimal), and p is a prime that does not divide b. (Primes p that give cyclic numbers in base b are called full reptend primes or long primes in base b). For example, the case b = 10, p = 7 gives the cyclic number 142857, and the case b = 12, p = 5 gives the cyclic number 2497.
The secondary functional groups are: a hydroxy- at carbon 5, a chloro- at carbon 11, a methoxy- at carbon 15, and a bromo- at carbon 18. Grouped with the side chains, this gives 18-bromo-12-butyl-11-chloro-4,8-diethyl-5-hydroxy-15-methoxy. There are two double bonds: one between carbons 6 and 7, and one between carbons 13 and 14.
These numbers are arranged in descending order and are separated by periods. For example, the carbon frame of norbornane contains a total of 7 atoms, hence the root name heptane. This molecule has two paths of 2 carbon atoms and a third path of 1 carbon atom between the two bridgehead carbons, so the brackets are filled in descending order: [2. ...
If p is a prime number, then any group with p elements is isomorphic to the simple group Z/pZ. A number n is called a cyclic number if Z/nZ is the only group of order n, which is true exactly when gcd(n, φ(n)) = 1. [13] The sequence of cyclic numbers include all primes, but some are composite such as 15. However, all cyclic numbers are odd ...
A cyclic number [1] [2] is a natural number n such that n and φ(n) are coprime. Here φ is Euler's totient function. An equivalent definition is that a number n is cyclic if and only if any group of order n is cyclic. [3] Any prime number is clearly cyclic. All cyclic numbers are square-free. [4] Let n = p 1 p 2 …