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Integer whose multiples are digit rotations
cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely-known cyclic number
Cyclic_number
Decimal representation of a number whose digits are periodic
also the article 142,857 for more properties of this cyclic number. A fraction which is cyclic thus has a recurring decimal of even length that divides
Repeating_decimal
Natural number, cyclic number
natural number following 142,856 and preceding 142,858. It is both a Kaprekar number and a cyclic number. 142857 is the best-known cyclic number in base
142857
Number n where n and totient(n) are coprime
definition is that a number n is cyclic if and only if any group of order n is cyclic. Any prime number is clearly cyclic. All cyclic numbers are square-free.
Cyclic_number_(group_theory)
Mathematical group that can be generated as the set of powers of a single element
In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused
Cyclic_group
Index of articles associated with the same name
begin with cyclic: Cyclic chain rule, for derivatives, used in thermodynamics Cyclic code, linear codes closed under cyclic permutations Cyclic convolution
Cyclic_(mathematics)
Number that when multiplied by another number moves its last digit to its front
219, 32, 48, 66, 239, 81, 498, ... (sequence A128858 in the OEIS) Cyclic number Linear-feedback shift register Transposable integer Dawidoff, Nicholas
Parasitic_number
Natural number
Markov number 142,129 = 3772, square number, dodecagonal number 142,857 = Kaprekar number, smallest cyclic number in decimal. 144,000 = number with religious
100,000
Molecule with a ring of bonded atoms
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:
Cyclic_compound
Natural number
(111) and base 18 (77), whilst in base 20 it is a cyclic number formed from the reciprocal of the number three. 133 is a semiprime: a product of two prime
133_(number)
Number that permute or shift cyclically when multiplied by another number
or shift cyclically when they are multiplied by another integer n {\displaystyle n} . Examples are: 142857 × 3 = 428571 (shifts cyclically one place
Transposable_integer
Natural number
= Motzkin number 157,115,917 = number of parallelogram polyominoes with 24 cells. 165,580,141 = Fibonacci number 167,444,795 = cyclic number in base 6
100,000,000
Class of prime numbers
b) gives a cyclic number. Therefore, the base b expansion of 1 / p {\displaystyle 1/p} repeats the digits of the corresponding cyclic number infinitely
Full_reptend_prime
Sequence of numbers
cyclic number with p − 1 digits. Therefore, the base b expansion of 1 / p {\displaystyle 1/p} repeats the digits of the corresponding cyclic number infinitely
Reciprocals_of_primes
cubes in two different ways. 8128, the fourth perfect number. 142857, the smallest base 10 cyclic number. 9814072356, the largest perfect power that contains
List_of_numbers
Mathematical group based upon a finite number of elements
objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups
Finite_group
Natural number
cyclic number in base 6 5,555,555 = repdigit 5,623,756 = number of trees with 22 unlabelled nodes 5,702,887 = Fibonacci number 5,761,455 = the number
1,000,000
Error-detecting code for detecting data changes
A cyclic redundancy check (CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital
Cyclic_redundancy_check
Galois extension whose Galois group is abelian
In algebraic number theory, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension
Abelian_extension
Type of (mathematical) permutation with no fixed element
theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation
Cyclic_permutation
Cellular second messenger
Cyclic adenosine monophosphate (cAMP, cyclic AMP, or 3',5'-cyclic adenosine monophosphate) is a second messenger, or cellular signal occurring within
Cyclic adenosine monophosphate
Cyclic_adenosine_monophosphate
379, 389, 401, 409 (OEIS: A109611) A circular prime is a number that remains prime on any cyclic rotation of its base 10 digits. 2, 3, 5, 7, 11, 13, 17
List_of_prime_numbers
Natural number
super-prime 4139 – safe prime 4140 – Bell number 4141 – centered square number 4147 – smallest cyclic number in duodecimal represented in base-12 notation
4000_(number)
Natural number
dual positions with the vertices of another tetrahedron. The smallest non-cyclic group has four elements; it is the Klein four-group. An alternating groups
4
Convex hull of points on moment curve
McMullen and Richard Stanley, the boundary Δ(n,d) of the cyclic polytope C(n,d) maximizes the number fi of i-dimensional faces among all simplicial spheres
Cyclic_polytope
Alternative mathematical ordering
with a cyclic order is called a cyclically ordered set or simply a cycle.[nb] Some familiar cycles are discrete, having only a finite number of elements:
Cyclic_order
Peptide chains which contain a circular sequence of bonds
Cyclic peptides are polypeptide chains which contain a circular sequence of bonds. This can be through a connection between the amino and carboxyl ends
Cyclic_peptide
Composite number in number theory
Fermat witness for any even composite number.) From the criterion it also follows that Carmichael numbers are cyclic. Additionally, it follows that there
Carmichael_number
Concept in Number Theory
the multiplicative group of integers modulo p, then qp(a) will be a cyclic number, and p will be a full reptend prime. From the definition, it is obvious
Fermat_quotient
Irreducible fraction = in lowest terms Dyadic fraction Recurring decimal Cyclic number Farey sequence Ford circle Stern–Brocot tree Dedekind sum Egyptian fraction
List_of_number_theory_topics
In combinatorial mathematics, cyclic sieving is a phenomenon in which an integer polynomial evaluated at certain roots of unity counts the rotational symmetries
Cyclic_sieving
Number in {..., –2, –1, 0, 1, 2, ...}
\mathbb {Z} } under addition is the only infinite cyclic group—in the sense that any infinite cyclic group is isomorphic to Z {\displaystyle \mathbb
Integer
Cyclic nucleic acid
A cyclic nucleotide (cNMP) is a single-phosphate nucleotide with a cyclic bond arrangement between the sugar and phosphate groups. Like other nucleotides
Cyclic_nucleotide
Natural number
nineteen) is the natural number following 118 and preceding 120. 119 is a Perrin number. 119 is the order of the largest cyclic subgroups of the monster
119_(number)
Chemical compound
Cyclic ozone is a theoretically predicted form of ozone. Like ordinary ozone (O=O+−O−), it would have three oxygen atoms. It would differ from ordinary
Cyclic_ozone
Chemical compound
Cyclic di-GMP (also called cyclic diguanylate and c-di-GMP) is a second messenger used in signal transduction in a wide variety of bacteria. Cyclic di-GMP
Cyclic_di-GMP
In algebra, a cyclic division algebra is one of the basic examples of a division algebra over a field and plays a key role in the theory of central simple
Cyclic_algebra
Pattern of vegetation change
Cyclic succession is a pattern of vegetation change in which in a small number of species tend to replace each other over time in the absence of large-scale
Cyclic_succession
Used to count, measure, and label
is 0.02. If the fractional part of a real number has an infinite sequence of digits that follows a cyclical pattern, it can be written with an ellipsis
Number
Type of flower having many whorls
arranged sepals on an otherwise cyclic flower, the term hemicyclic may be used. The suffix -cyclic is used to denote the number of whorls contained within
Cyclic_flower
noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras
Cyclic_homology
Theorem in number theory
In number theory, the Hasse norm theorem states that if L/K is a cyclic extension of number fields, then if a nonzero element of K is a local norm everywhere
Hasse_norm_theorem
Conjecture in number theory
constant plays here Brown–Zassenhaus conjecture Full reptend prime Cyclic number (group theory) Michon, Gerard P. (2006-06-15). "Artin's Constant". Numericana
Artin's conjecture on primitive roots
Artin's_conjecture_on_primitive_roots
Chemical compound
Cyclic guanosine monophosphate (cGMP) is a cyclic nucleotide derived from guanosine triphosphate (GTP). cGMP acts as a second messenger much like cyclic
Cyclic guanosine monophosphate
Cyclic_guanosine_monophosphate
Number used for counting
natural-number results: subtracting a larger natural number from a smaller one results in a negative number and dividing one natural number by another
Natural_number
Points on a common circle
For a cyclic polygon with an odd number of sides, all angles are equal if and only if the polygon is regular. A cyclic polygon with an even number of sides
Concyclic_points
Shape with five sides
symmetry, order 10. Since 5 is a prime number, there is one subgroup with dihedral symmetry: Dih1, and 2 cyclic group symmetries: Z5, and Z1. These 4 symmetries
Pentagon
Human disease
Cyclic vomiting syndrome (CVS) is a chronic functional condition of unknown pathogenesis. CVS is characterized as recurring episodes lasting a single day
Cyclic_vomiting_syndrome
Medical condition
Cyclic neutropenia (CyN) is a rare hematologic disorder and form of congenital neutropenia that tends to occur approximately every three weeks and lasting
Cyclic_neutropenia
Chemical compound
5'-cyclic adenosine monophosphate (8-Br-cAMP) is a brominated derivative of cyclic adenosine monophosphate (cAMP). 8-Br-cAMP is an activator of cyclic AMP-dependent
8-Bromoadenosine 3',5'-cyclic monophosphate
8-Bromoadenosine_3',5'-cyclic_monophosphate
them. It was introduced by Connes (1983). The cyclic category Λ has one object Λn for each natural number n = 0, 1, 2, ... The morphisms from Λm to Λn
Cyclic_category
Chemical compound
Cyclic di-AMP (also called c-di-AMP and c-di-adenosine monophosphate) is a second messenger used in signal transduction in bacteria and archaea. It is
Cyclic_di-AMP
Number equal to the sum of its proper divisors
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number
Perfect_number
used to label the group within that order. Common group names: Zn: the cyclic group of order n (the notation Cn is also used; it is isomorphic to the
List_of_small_groups
Deterministic model of computation
H = 001) Cyclic tag system Productions: (010 010, 100 010 001, 001, -, -, -) Tag system computation Initial word: ba abH Hbb (halt) Cyclic tag system
Tag_system
Numbers obtained by adding the two previous ones
month, the number of pairs of rabbits is equal to the number of mature pairs (that is, the number of pairs in month n – 2) plus the number of pairs alive
Fibonacci_sequence
Topics referred to by the same term
cycle, cyclic, or cyclical in Wiktionary, the free dictionary. Cycle, cycles, or cyclic may refer to: Cyclic history, a theory of history Cyclical theory
Cycle
Number
A Brain for Numbers: The Biology of the Number Instinct. MIT Press. p. 286. Reimer 2014, p. 172. "Cyclical views of time". www.mexicolore.co.uk. Retrieved
0
Type of sediment wave
be used to create cyclic steps in subaerial laboratory conditions, provided the Froude number is high enough. If the Froude number is lower than required
Cyclic_steps
Online mathematics resource for cubic plane curves
more succinctly in "cyclic sum notation", like this: ∑ cyclic f ( x , y , z , a , b , c ) = 0 {\displaystyle \sum _{\text{cyclic}}f(x,y,z,a,b,c)=0} .
Catalogue_of_Triangle_Cubics
Terpene hydrocarbon
(/ˈlɪmənˌiːn/) is a colorless liquid aliphatic hydrocarbon classified as a cyclic monoterpene, and is the major component in the fragrance and essential oil
Limonene
Number divisible only by 1 and itself
order is a cyclic group, and by Burnside's theorem any group whose order is divisible by only two primes is solvable. For a long time, number theory in
Prime_number
field K is called a cyclic cubic field if it contains all three roots of its generating polynomial f. Equivalently, K is a cyclic cubic field if it is
Cubic_field
System of digitally encoding numbers
false state as it is delayed in going from one cyclic number to the next. There are many other cyclic codes that have this property. […] {{cite book}}:
Binary-coded_decimal
Chemical compound
peroxide and a strong acidic catalyst to yield a mixture of linear monomer and cyclic dimer, trimer, and tetramer forms. The monomer is dimethyldioxirane. The
Acetone_peroxide
Mathematical concept and applications in software development
performing the inverse operation. A circular shift is a special kind of cyclic permutation, which in turn is a special kind of permutation. Formally, a
Circular_shift
Chemical compound
Cyclic olefin polymer (COP) is a type of amorphous polymer used in a wide variety of applications including pharmaceutical packaging and medical devices
Cyclic_olefin_polymer
Integer having a non-trivial divisor
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly, it is a positive integer that has
Composite_number
Chemical compound
Cyclic olefin copolymer (COC) is an amorphous polymer made by several polymer manufacturers. COC is a relatively new class of polymers as compared to commodities
Cyclic_olefin_copolymer
Chemical compound
abbreviated PC) is an organic compound with the formula C4H6O3. It is a cyclic carbonate ester derived from propylene glycol. This colorless and odorless
Propylene_carbonate
Figurate number
The triangular lattice representing the n {\displaystyle n} th triangular number contains n {\displaystyle n} rows: the first row contains one point, the
Triangular_number
Computation of a cyclic redundancy check is derived from the mathematics of polynomial division, modulo two. In practice, it resembles long division of
Computation of cyclic redundancy checks
Computation_of_cyclic_redundancy_checks
Chemical compound
Cyclic guanosine monophosphate–adenosine monophosphate (cyclic GMP-AMP, cGAMP) is the first cyclic di-nucleotide found in metazoa. In mammalian cells,
Cyclic guanosine monophosphate–adenosine monophosphate
Cyclic_guanosine_monophosphate–adenosine_monophosphate
Shape with six sides
\mathrm {t} \{3\}} . A regular hexagon is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The
Hexagon
Natural number
integers that adds to 11, counting two sums as equivalent when they are cyclic permutations of each other. There are also 187 unordered triples of 5-bit
187_(number)
Group of units of the ring of integers modulo n
|(\mathbb {Z} /n\mathbb {Z} )^{\times }|=\varphi (n).} For prime n the group is cyclic, and in general the structure is easy to describe, but no simple general
Multiplicative group of integers modulo n
Multiplicative_group_of_integers_modulo_n
Elementary cellular automaton
emulate another computational model, the cyclic tag system, which is known to be universal. He first isolated a number of spaceships, self-perpetuating localized
Rule_110
Type of group in mathematics
mathematics, a primary cyclic group is a group that is both a cyclic group and a p-primary group for some prime number p. That is, it is a cyclic group of order
Primary_cyclic_group
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
undirected graph acted on by a cyclic group of symmetries which takes any vertex to any other vertex. It is sometimes called a cyclic graph, but this term has
Circulant_graph
Theory of political fluctuations in US history
Cyclical theories of history are intended to explain the numerous recurring events and patterns in humanity's recorded history. Several such cycles and
Cyclical_theory
theorem states that cyclic polytopes have the largest possible number of faces among all convex polytopes with a given dimension and number of vertices. It
Upper_bound_theorem
Numbers whose aliquot sums form a cyclic sequence
sequence must be cyclic and return to its starting point. The period of the sequence, or order of the set of sociable numbers, is the number of numbers in
Sociable_number
Mathematical object
class of lattices and a generalization of cyclic lattices. Ideal lattices naturally occur in many parts of number theory, but also in other areas. In particular
Ideal_lattice
Natural number
Sequences. OEIS Foundation. Retrieved 2016-05-29. Numbers such that every cyclic permutation is a prime. "Sloane's A035497 : Happy primes". The On-Line Encyclopedia
79_(number)
Small neuroactive peptide
Cyclic glycine-proline (cGP) is a small neuroactive peptide that belongs to a group of bioactive 2,5-diketopiperazines (2,5-DKPs) and is also known as
Cyclic_glycine-proline
Type of block code
In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting
Cyclic_code
Integer having only small prime factors
In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is
Smooth_number
Product of an integer with itself
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with
Square_number
A cyclic cellular automaton is a kind of cellular automaton rule developed by David Griffeath and studied by several other cellular automaton researchers
Cyclic_cellular_automaton
Chemical compound
trifluoromethanesulfonic anhydride, to selectively and rapidly nitrate cyclic (number of atoms in the ring is 5 or 6), aromatic and heteroaromatic compounds
Tetramethylammonium_nitrate
Area of a right triangle with rational-numbered sides
In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. A more general definition
Congruent_number
Composite number with special property
In number theory, an n-Knödel number for a given positive integer n is a composite number m with the property that each i < m coprime to m satisfies i
Knödel_number
Graph with nodes connected in a closed chain
are many synonyms for "cycle graph". These include simple cycle graph and cyclic graph, although the latter term is less often used, because it can also
Cycle_graph
Type of prime number
A circular prime is a prime number with the property that the number generated at each intermediate step when cyclically permuting its (base 10) digits
Circular_prime
Methods of error detection and correction in communications
The cyclic redundancy check (CRC) is a check of the remainder after division in the ring of polynomials over GF(2) (the finite field of integers modulo
Mathematics of cyclic redundancy checks
Mathematics_of_cyclic_redundancy_checks
Mathematics of number-placement puzzle
such as "How many filled Sudoku grids are there?", "What is the minimal number of clues in a valid puzzle?" and "In what ways can Sudoku grids be symmetric
Mathematics_of_Sudoku
Base-dependent property of integers
In mathematics, a natural number in a given number base is a p {\displaystyle p} -Kaprekar number if the representation of its square in that base can
Kaprekar_number
Chemical compound
arrangements are known: a linear form with double bonds and charge transfer, and a cyclic form. Both forms are highly unstable, though the linear form is the more
Trinitrogen
Natural number
as 170! = 7.25741562 × 10306.[citation needed] There are 170 different cyclic Gilbreath permutations on 12 elements, and therefore there are 170 different
170_(number)
Number with an integer power equal to 1
multiplication a cyclic group of order n, and in fact these groups comprise all of the finite subgroups of the multiplicative group of the complex number field.
Root_of_unity
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