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Number that represents a hexagon with a dot in the center
combinatorics, a centered hexagonal number, or centered hexagon number, is a centered figurate number that represents a hexagon with a dot in the center and all
Centered_hexagonal_number
Type of figurate number
A hexagonal number is a figurate number. The nth hexagonal number hn is the number of distinct dots in a pattern of dots consisting of the outlines of
Hexagonal_number
Natural number
numbers to also be a centered hexagonal number. a centered nonagonal number. a centered cube number. a square pyramidal number, being the sum of the squares
91_(number)
One of the five 2D Bravais lattices
Square lattice (see dots in a diagonal square centered) Hexagonal tiling Close-packing Centered hexagonal number Eisenstein integer Voronoi diagram Hermite
Hexagonal_lattice
Natural number
two consecutive squares, 52+62. It is also a centered decagonal number, and a centered hexagonal number. 61 is the fourth cuban prime of the form p=x3−y3x−y
61_(number)
Natural number
primes; thus, it is a strong prime. 127 is a centered hexagonal number. It is the seventh Motzkin number. 127 is a palindromic prime in nonary and binary
127_(number)
Type of prime number
is exactly the general form of a centered hexagonal number; that is, all of these cuban primes are centered hexagonal. As of July 2023[update] the largest
Cuban_prime
Figurate number
numbers are closely related to centered hexagonal numbers. When the array corresponding to a centered hexagonal number is divided between its middle row
Pentagonal_number
Natural number
number with an irregularity index of 2 is the thirty-seventh prime number, 157. 37 is the third star number and the fourth centered hexagonal number.
37_(number)
Natural number
squares to also be a centered hexagonal number. Like all odd squares, it is a centered octagonal number. 169 is an odd-indexed Pell number, thus it is also
169_(number)
Natural number
a centered hexagonal number. It is the smallest prime number bracketed on both sides by numbers divisible by cubes, and the smallest prime number bracketed
271_(number)
Natural number
is a centered hexagonal number and the sum of nine consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101). It is the smallest number that is
700_(number)
Natural number
natural number following 299 and preceding 301. 300 is a composite number and the 24th triangular number. It is also a second hexagonal number. 300 is
300_(number)
Class of series of figurate numbers, each having a central dot
n2 + (n − 1)2. centered pentagonal numbers 1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, ... (OEIS: A005891), centered hexagonal numbers 1, 7, 19
Centered_polygonal_number
Natural number
prime number, a Cuban prime, a Lucky prime a Chen prime, a centered triangular number, a centered hexagonal number, and a lazy caterer number (sequence
600_(number)
Natural number
It is a centered hexagonal number. 469! - 1 is prime. 470 = 2 × 5 × 47. It is a sphenic number, a nontotient, a noncototient, and a cake number. 471 =
400_(number)
Natural number
× 17. It is a tetrahedral number, a Padovan number, and a Zuckerman number. 817 = 19 × 43. It is a centered hexagonal number and the sum of three consecutive
800_(number)
Centered figurate number that represents a triangle with a dot in the center
other dots surrounding the center in successive equilateral triangular layers. This is also the number of points of a hexagonal lattice with nearest-neighbor
Centered_triangular_number
Natural number
is the natural number following 216 and preceding 218. 217 is a centered hexagonal number, a 12-gonal number, a centered 36-gonal number, a Fermat pseudoprime
217_(number)
number Centered polygonal number Centered square number Centered pentagonal number Centered hexagonal number Tetrahedral number Pyramidal number Triangular
List of recreational number theory topics
List_of_recreational_number_theory_topics
Centered figurate number
also called centered dodecagonal numbers because star numbers are centered polygonal numbers with a twelve-sided shape. The nth star number is given by
Star_number
Natural number
number following 27 and preceding 29. 28 is a composite number, a perfect number, a harmonic divisor number, a centered nonagonal number, a hexagonal
28_(number)
Natural number
546! − 1 is prime. 547 is a prime number, a cuban prime, a centered hexagonal number, a centered heptagonal number, and a prime index prime. 548 = 22
500_(number)
Natural number
centered hexagonal number 4225 = 652, centered octagonal number 4227 – sum of the first 46 primes 4240 – Leyland number 4257 – decagonal number 4259 – safe
4000_(number)
Natural number
number, the 35th square number, the 25th hexagonal number, a centered octagonal number, a 29-gonal number, a 60-gonal number, and a 124-gonal number.
1000_(number)
Type of figurate number
nth hexagonal number P(6,n) is also the (2n − 1)th triangular number T2n−1. We can find every hexagonal number by simply taking the odd-numbered triangular
Polygonal_number
Natural number
number following 189 and preceding 191. 190 is a triangular number, a hexagonal number, and a centered nonagonal number, the fourth figurate number (after
190_(number)
Shape with six sides
cuboids. A regular hexagon has Schläfli symbol {6}. A regular hexagon is a part of the regular hexagonal tiling, {6,3}, with three hexagonal faces around each
Hexagon
Regular tiling of a two-dimensional space
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex
Hexagonal_tiling
Natural number
ways than any smaller number. 32760 = harmonic divisor number 32761 = 1812, centered hexagonal number 32767 = 215 − 1, largest positive value for a signed
30,000
Cloud pattern on the planet Saturn
Saturn's hexagon is a persistent approximately hexagonal cloud pattern around the north pole of the planet Saturn, located at about 78°N. The sides of
Saturn's_hexagon
Union of crystal groups with related structures and lattices
In crystallography, the hexagonal crystal family is one of the six crystal families; it includes two crystal systems (hexagonal and trigonal) and two lattice
Hexagonal_crystal_family
Number, product of consecutive integers
pronic number. The nth pronic number is also the difference between the odd square (2n + 1)2 and the (n+1)st centered hexagonal number. Since the number of
Pronic_number
Centered figurate number that represents a pentagon with a dot in the center
In mathematics, a centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding
Centered_pentagonal_number
Figurate number
triangular number is a hexagonal number. Knowing the triangular numbers, one can reckon any centered polygonal number; the nth centered k-gonal number is obtained
Triangular_number
Classification of crystalline materials by their three-dimensional structural geometry
groups assigned to the hexagonal lattice system. These point groups are assigned to the trigonal crystal system. The hexagonal and trigonal crystal systems
Crystal_system
Dense arrangement of congruent spheres in an infinite, regular arrangement
face-centered cubic lattices, but with different orientations to the ground. Hexagonal close-packing would result in a pyramid with a hexagonal base.
Close-packing of equal spheres
Close-packing_of_equal_spheres
Figurate number
550, 726, 936, 1183, ... (sequence A002411 in the OEIS). The first few hexagonal pyramidal numbers are: 1, 7, 22, 50, 95, 161, 252, 372, 525, 715, 946
Pyramidal_number
Crystallography concept
packing fraction. Hexagonal close-packed (HCP): 0.74 Face-centered cubic (FCC): 0.74 (also called cubic close-packed, CCP) Body-centered cubic (BCC): 0.68
Atomic_packing_factor
Number of dots in a centred dot square
elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all
Centered_square_number
Prism with a 6-sided base
In geometry, the hexagonal prism is a prism with hexagonal base. this polyhedron has 8 faces, 18 edges, and 12 vertices. A hexagonal prism has twelve
Hexagonal_prism
Natural number
icosahedral number, the 33rd triangular number, and the 17th hexagonal number. It is a composite number, with the divisors being 1, 3, 11, 17, 33, 51, 187, and
561_(number)
Natural number
groups J1 and J3. 19 is a Heegner number. The James Webb Space Telescope's optical elements are in an array of 19 hexagons, wherein 18 segmented primary mirrors
19_(number)
Centered figurate number that represents a heptagon with a dot in the center
A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center
Centered_heptagonal_number
Natural number
5th triangular number, a hexagonal number, and pentadecagonal number. It is also a centered tetrahedral number. 15 is a lucky number. 15 is the smallest
15_(number)
Map subdivided into a hexagonal tiling, small regular hexagons of identical size
games and video games. A hex map is subdivided into a hexagonal tiling, small regular hexagons of identical size. The primary advantage of a hex map over
Hex_map
Natural number
496. It is also a triangular and a hexagonal number. and a centered nonagonal number. Being the 31st triangular number, 496 is the smallest counterexample
496_(number)
Centered figurate number that represents an octagon with a dot in the center
centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center
Centered_octagonal_number
Arrangement of numbers
A magic hexagon of order n is an arrangement of numbers in a centered hexagonal pattern with n cells on each edge, in such a way that the numbers in each
Magic_hexagon
Centered figurate number that represents a decagon with a dot in the center
centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot
Centered_decagonal_number
Natural number
natural number following 230 and preceding 232. 231 is a sphenic number. 231 is the 21st triangular number, a doubly triangular number, a hexagonal number, an
231_(number)
Number used to approximate the square root of 2
starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number, plus the Pell number before that. The first few terms of the
Pell_number
Centered figurate number that represents a nonagon with a dot in the center
A centered nonagonal number, (or centered enneagonal number), is a centered figurate number that represents a nonagon with a dot in the center and all
Centered_nonagonal_number
Three-dimensional figurate centered icosahedral numbers
of a cuboctahedron, and are a magic number for the face-centered cubic lattice. The centered icosahedral number for a specific n {\displaystyle n} is
Centered_icosahedral_number
Geometric pattern used in art
n^{3}-(n-1)^{3}=3n^{2}-3n+1=3n(n-1)+1} , where n is the number of rings, forming the centered hexagonal numbers. These overlapping circles can also be seen
Overlapping_circles_grid
Natural number
53. It is a centered triangular number and a happy number. 902 = 2 × 11 × 41. It is a sphenic number, a nontotient, and a Harshad number. 903 = 3 × 7
900_(number)
Centered figurate number representing a tetrahedron
In mathematics, a centered tetrahedral number is a centered figurate number that represents a tetrahedron. That is, it counts the dots in a three-dimensional
Centered_tetrahedral_number
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
Centered figurate number that counts points in a three-dimensional pattern
is the number of points in a body-centered cubic pattern within a cube that has n + 1 points along each of its edges. The first few centered cube numbers
Centered_cube_number
Number equal to the sum of its proper divisors
perfect number is the (2p−1)-th triangular number (and hence equal to the sum of the integers from 1 to 2p−1) and the 2p−1-th hexagonal number. Furthermore
Perfect_number
Number divisible only by 1 and itself
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that
Prime_number
Product of an integer with itself
Every odd square is also a centered octagonal number. Another property of a square number is that (except 0) it has an odd number of positive divisors, while
Square_number
Topics referred to by the same term
Jersey) Farm to Market Road 721 Saskatchewan Highway 721 721 (number), a centered hexagonal number 721 Tabora, a carbonaceous asteroid from the outer regions
721_(disambiguation)
Size of a geometric arrangement of points
= 82. There is a similar gnomon with centered hexagonal numbers adding up to make cubes of each integer number. Dickson, L. E. (1919), History of the
Figurate_number
Natural number with a decimal representation made of repeated instances of the same digit
or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The
Repdigit
Iterative algorithm on numbers
In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with
Kaprekar's_routine
Centered figurate number representing an octahedron
In mathematics, a centered octahedral number or Haüy octahedral number is a figurate number that counts the points of a three-dimensional integer lattice
Centered_octahedral_number
Ten raised to an integer power
the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one
Power_of_10
Hexaferrite
Hexagonal ferrites or hexaferrites are a family of ferrites with hexagonal crystal structure. The most common member is BaFe12O19, also called barium ferrite
Hexagonal_ferrite
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
Numbers that contain only the digit 1
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands
Repunit
Two raised to an integer power
A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with the number 2 as the base and integer n as the
Power_of_two
Arithmetic operation
extended in a natural way to define bx for any positive real number base b and any real number exponent x. A more involved definition supports arbitrary
Exponentiation
Integer with a specific property
In number theory, a Sierpiński number is an odd natural number k such that k×2n+1 is composite for all natural numbers n. In 1960, Wacław Sierpiński proved
Sierpiński_number
Crystallographic system where the unit cell is in the shape of a cube
placements of their hexagonal layers. The [111] plane of a face-centered cubic lattice is a hexagonal grid. Attempting to create a base-centered cubic lattice
Cubic_crystal_system
Swedish tech company
Hexagon AB is a multinational industrial technology company. Headquartered in Stockholm, Sweden, and publicly traded on the Nasdaq Stockholm exchange
Hexagon_AB
Natural number
(1^{3}+2^{3})(1^{3}+3^{3})=252.} a practical number, a refactorable number, a hexagonal pyramidal number. a member of the Mian-Chowla sequence. There
252_(number)
Refractory compound of boron and nitrogen with formula BN
crystalline form is the hexagonal one, also called h-BN, α-BN, g-BN, graphitic boron nitride and "white graphite". Hexagonal boron nitride (point group
Boron_nitride
Recursive integer sequence
triangulation). The number of triangles formed is n and the number of different ways that this can be achieved is Cn. The following hexagons illustrate the
Catalan_number
Natural number
octahedral number; 8119/5741 ≈ √2 8125 – pentagonal pyramidal number 8128 – perfect number, harmonic divisor number, 127th triangular number, 64th hexagonal number
8000_(number)
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
Antiprism with 6-sided caps
semiregular polyhedron. A crossed hexagonal antiprism is a star polyhedron, topologically identical to the convex hexagonal antiprism with the same vertex
Hexagonal_antiprism
Type of figurate number
additional layer. Centered tetrahedral numbers Centered cube numbers Centered octahedral numbers Centered dodecahedral numbers Centered icosahedral numbers
Centered_polyhedral_number
Math theorem about sphere packing
average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements. The density of these arrangements
Kepler_conjecture
Prime number of the form 2^n – 1
mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer
Mersenne_prime
Number that remains the same when its digits are reversed
A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16361) that remains the same when its digits are
Palindromic_number
Crystalline structure for solid elements
layers: Mg type (hexagonal close packing) has alternate layers positioned directly above/below each other: A,B,A,B,... Cu type (face-centered cubic) has every
Periodic table (crystal structure)
Periodic_table_(crystal_structure)
Numbers with a certain property involving recursive summation
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance
Happy_number
Number that is less than the sum of its proper divisors
In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The
Abundant_number
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
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 in number theory
In number theory, a Carmichael number is a composite number n which in modular arithmetic satisfies the congruence relation: bn≡b(modn) for all integers
Carmichael_number
of the order-5 hexagonal tiling honeycomb is {6,3,5}. Since that of the hexagonal tiling is {6,3}, this honeycomb has five such hexagonal tilings meeting
Order-5 hexagonal tiling honeycomb
Order-5_hexagonal_tiling_honeycomb
Positive integer of the form (2^(2^n))+1
In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have studied them, is a positive integer of the form: Fn=22n+1
Fermat_number
of the hexagonal tiling honeycomb is {6,3,6}. Since that of the hexagonal tiling of the plane is {6,3}, this honeycomb has six such hexagonal tilings
Order-6 hexagonal tiling honeycomb
Order-6_hexagonal_tiling_honeycomb
Integer divisible by sum of its digits
In recreational mathematics, a Harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written
Harshad_number
Concept in number theory
In number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number (after Michael F. Armstrong) or a plus
Narcissistic_number
Numbers k where x - phi(x) = k has many solutions
In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above 1 and has more solutions to the equation x−ϕ(x)=k
Highly_cototient_number
Class of natural numbers with many divisors
In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it is
Superior highly composite number
Superior_highly_composite_number
Integer filtered out using a sieve similar to that of Eratosthenes
In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the sieve of Eratosthenes
Lucky_number
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CENTERED HEXAGONAL-NUMBER
CENTERED HEXAGONAL-NUMBER
CENTERED HEXAGONAL-NUMBER
CENTERED HEXAGONAL-NUMBER
CENTERED HEXAGONAL-NUMBER
CENTERED HEXAGONAL-NUMBER
CENTERED HEXAGONAL-NUMBER
CENTERED HEXAGONAL-NUMBER
CENTERED HEXAGONAL-NUMBER
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