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Figurate number representing a decagon
In mathematics, a decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon)
Decagonal_number
Centered figurate number that represents a decagon with a dot in the center
A 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
Centered_decagonal_number
Natural number
a centered pentagonal number, and a centered decagonal number. 1056 = 25 × 3 × 11. It is a pronic number. 1060 = 22 × 5 × 53. It is the sum of the first
1000_(number)
Natural number
(four thousand) is the natural number following 3999 and preceding 4001. It is a decagonal number. 4005 – triangular number 4007 – safe prime 4010 – magic
4000_(number)
Natural number
Mersenne number that is composite for a prime exponent. It is a super-Poulet number, a Woodall number, a decagonal number, and a centered octahedral number. 2053
2000_(number)
Natural number
Kaprekar number, 5051 – Sophie Germain prime 5059 – super-prime 5076 – decagonal number 5081 – Sophie Germain prime 5087 – safe prime 5099 – safe prime 5107
5000_(number)
Natural number
as 25 - 1. 31 is a centered triangular number, a centered pentagonal number, and a centered decagonal number. 31 equal temperament is a popular microtonal
31_(number)
Natural number
octagonal number, dodecagonal number 3037 – star number, cousin prime with 3041 3046 – centered heptagonal number 3052 – decagonal number 3059 – centered
3000_(number)
Natural number
heptagonal number 7247 – safe prime 7260 – triangular number 7267 – decagonal number 7272 – Kaprekar number 7283 – super-prime 7291 – nonagonal number 7310
7000_(number)
Natural number
Since 913 is a semiprime, 911 is a Chen prime. It is also a centered decagonal number. There are 911 inverse semigroups of order 7. 911 is obtained by concatenating
900_(number)
Natural number
is a decagonal number and a zero of the Mertens function. 638 = 2 × 11 × 29. It is a sphenic number, a nontotient, a centered heptagonal number, and the
600_(number)
Natural number
centered octagonal number 6250 – Leyland number 6263 – Sophie Germain prime, balanced prime 6269 – Sophie Germain prime 6280 – decagonal number 6311 – super-prime
6000_(number)
Natural number
octagonal number 9029 – Sophie Germain prime 9041 – super-prime 9045 – triangular number 9059 – Sophie Germain prime 9072 – decagonal number 9077 – Markov
9000_(number)
Natural number
23,1,0). an octahedral number. a centered triangular number. a centered square number. a decagonal number. the smallest number that can be expressed as
85_(number)
Natural number
it is not equal to x − φ(x) for any x . 52 is a decagonal number and a vertically symmetrical number. "Bell, or exponential numbers". The On-Line Encyclopedia
52_(number)
Natural number
nonagonal number, centered octagonal number 8287 – super-prime 8321 – super-Poulet number 8326 – decagonal number 8345 – smallest pandigital number in base
8000_(number)
Natural number
number and the 38th triangular number. 742 = 2 × 7 × 53. It is a sphenic number, a decagonal number, an icosahedral number, and a lazy caterer number
700_(number)
Natural number
strictly non-palindromic number. 361 = 192. 361 is a centered triangular number, a centered octagonal number, a centered decagonal number and a member of the
300_(number)
Natural number
twin prime. 151 is also a palindromic prime, a centered decagonal number, and a lucky number. 151 appears in the Padovan sequence, preceded by the terms
151_(number)
Natural number
number and a nontotient. There are 854 unlabeled planar trees with 11 nodes. 855 = 32 × 5 × 19. It is a decagonal number and a centered cube number.
800_(number)
Natural number
{\displaystyle 5^{2}+6^{2}} . It is also a centered decagonal number, and a centered hexagonal number. 61 is the fourth cuban prime of the form p = x 3
61_(number)
Natural number
figurate number for a rhombic dodecahedron, the difference of two consecutive fourth powers: 175 = 44 − 34. It is also a decagonal number and a decagonal pyramid
175_(number)
Natural number
is the natural number following 231 and preceding 233. 232 is both a central polygonal number, a decagonal number, and a cake number. It is both It is
232_(number)
Natural number
the only such Granville number. 126 is a pentagonal pyramidal number and a decagonal number. 126 is also the different number of ways to partition a decagon
126_(number)
Natural number
which has 48 divisors. It is also a regular number, a 3 times decagonal number, a number in base -3, and a number of the Hamiltonian cycles in the rook graph
12,000_(number)
Shape with ten sides
The number of sides in the Petrie polygon is equal to the Coxeter number, h, for each symmetry family. Decagonal number and centered decagonal number, figurate
Decagon
Natural number
22 × 33 × 5. It is a largely composite number, an untouchable number, a heptagonal number, and a decagonal number. It is the sum of a pair of twin primes
500_(number)
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
Natural number
prime factor of F12 115,975 = Bell number 116,281 = 3412, square number, centered decagonal number, 18-gonal number 117,067 = first vampire prime 117,649
100,000
Natural number
It is a Wedderburn–Etherington number and a centered decagonal number. It is the smallest number whose reciprocal has period 10. 452 = 22 × 113. There
400_(number)
Natural number
Chen prime, Eisenstein prime with no imaginary part, and a centered decagonal number. 281 is the smallest prime p such that the decimal period length of
281_(number)
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
Natural number
partitions of 17. 297 is a decagonal number which applies the properties of triangular numbers to decagons. 297 is a Kaprekar number which means that it can
297_(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
Natural number
introducing this concept. It is also a Fermat pseudoprime, a decagonal number, and a centered square number. It is a member of the Moser–de Bruijn sequence of sums
1105_(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
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
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
Odd number with specific properties
In number theory, a Sierpiński number is an odd natural number k such that k × 2 n + 1 {\displaystyle k\times 2^{n}+1} is composite for all natural numbers
Sierpiński_number
Polygonal number Triangular number Square number Pentagonal number Hexagonal number Heptagonal number Octagonal number Nonagonal number Decagonal number Centered
List of recreational number theory topics
List_of_recreational_number_theory_topics
Square of a triangular number
In number theory, the sum of the first n cubes is the square of the nth triangular number. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n ) 2
Squared_triangular_number
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
Polyhedral number representing a tetrahedron
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron
Tetrahedral_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
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
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
Recursive integer sequence
they were previously discovered in the 1730s by Minggatu. The n-th Catalan number can be expressed directly in terms of the central binomial coefficients
Catalan_number
Natural number
semiregular prisms (the triangular, pentagonal, hexagonal, octagonal, and decagonal prisms). 23 Coxeter groups of paracompact hyperbolic honeycombs in the
23_(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
Size of a geometric arrangement of points
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes
Figurate_number
Number that represents a hexagon with a dot in the center
mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, is a centered figurate number that represents a hexagon with a dot in the
Centered_hexagonal_number
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
Integer whose multiples are digit rotations
A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the
Cyclic_number
Number of form 2^(2^p-1)-1 with prime exponent
In mathematics, a double Mersenne number is a Mersenne number of the form M M p = 2 2 p − 1 − 1 {\displaystyle M_{M_{p}}=2^{2^{p}-1}-1} where p {\displaystyle
Double_Mersenne_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
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
Two or more natural numbers with a common abundancy index
In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and
Friendly_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
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
Number, non-palindrome after repeated sum with reverse
numbers exist? More unsolved problems in mathematics A Lychrel number is a natural number that cannot form a palindrome through the iterative process of
Lychrel_number
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
Type of figurate number
In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate
Polygonal_number
Number, product of consecutive integers
A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n ( n + 1 ) {\displaystyle n(n+1)} . The study
Pronic_number
Type of number introduced by Mike Keith
mathematics, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number n {\displaystyle n} in a given number base b {\displaystyle
Keith_number
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 two as the base and integer n as
Power_of_two
Number that when multiplied by another number moves its last digit to its front
In mathematics, an n-parasitic number (in base 10) is a positive natural number which, when multiplied by n, results in movement of the last digit of its
Parasitic_number
Number raised to the third power
algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number n is denoted n3,
Cube_(algebra)
Numbers that evenly divide powers of 60
and have different names coming from their different areas of study. In number theory, these numbers are called 5-smooth, because they can be characterized
Regular_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
Count of the possible partitions of a set
2,5,15,52,203,877,4140,\dots } (sequence A000110 in the OEIS). The Bell number B n {\displaystyle B_{n}} counts the different ways to partition a set that
Bell_number
Number of paths between grid corners, allowing diagonal steps
In mathematics, a Delannoy number D {\displaystyle D} counts the paths from the southwest corner (0, 0) of a rectangular grid to the northeast corner (m
Delannoy_number
Composite number in number theory
In number theory, a Carmichael number is a composite number n {\displaystyle n} which in modular arithmetic satisfies the congruence relation: b n
Carmichael_number
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
Numbers in a type of Lucas sequence
starts with 0 and 1, then each following number is found by adding the number before it to twice the number before that. The first Jacobsthal numbers
Jacobsthal_number
Number in the 5th cell of any row of Pascal's triangle
In number theory, a pentatope number (or hypertetrahedral number or triangulo-triangular number) is a number in the fifth cell of any row of Pascal's
Pentatope_number
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
Numbers whose sum of divisors is twice the number plus 1
unsolved problems in mathematics In mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the sum-of-divisors function
Quasiperfect_number
Type of figurate number
A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular and square numbers to the nonagon (a nine-sided
Nonagonal_number
Type of composite number with an even number of digits
recreational mathematics, a vampire number (or true vampire number) is a composite natural number with an even number of digits, that can be factored into
Vampire_number
Natural number
primes ( 67 + 71 + 73 {\displaystyle 67+71+73} ), a Chen prime, a centered decagonal prime, and a self prime. 211 is the smallest prime separated by 12 from
211_(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
Centered figurate number
In mathematics, a star number is a centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers
Star_number
Infinite integer series where the next number is the sum of the two preceding it
numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47
Lucas_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
Number that is more than the sum of its proper divisors
In number theory, a deficient number or defective number is a positive integer n for which the sum of divisors of n is less than 2n. Equivalently, it
Deficient_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
Positive integer with large prime factors
A k-rough number, as defined by Finch in 2001 and 2003, is a positive integer whose prime factors are all greater than or equal to k. k-roughness has alternately
Rough_number
Number of the form (n * 2^n) - 1
number theory, a Woodall number (Wn) is any natural number of the form W n = n ⋅ 2 n − 1 {\displaystyle W_{n}=n\cdot 2^{n}-1} for some natural number
Woodall_number
Class of series of figurate numbers, each having a central dot
(OEIS: A060544), which include all even perfect numbers except 6, centered decagonal numbers 1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, ... (OEIS: A062786)
Centered_polygonal_number
Concept in combinatorics
In mathematics, the cake number, denoted by Cn, is the maximum of the number of regions into which a 3-dimensional cube can be partitioned by exactly
Cake_number
Figurate number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns
Pentagonal_number
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
Number whose square ends in the same digits
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b {\displaystyle b} whose
Automorphic_number
Arithmetic operation
b x {\displaystyle b^{x}} for any positive real number base b {\displaystyle b} and any real number exponent x {\displaystyle x} . A more involved definition
Exponentiation
Number of stacked spheres in a pyramid
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid with a square base. The
Square_pyramidal_number
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: F n
Fermat_number
Product of two prime numbers
In number theory, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other
Semiprime
Numbers parameterizing ways to partition a set
particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
Type of Poulet number
In number theory, a super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor d {\displaystyle d} divides 2 d − 2 {\displaystyle
Super-Poulet_number
Type of integer in number theory
In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer
Polite_number
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DECAGONAL NUMBER
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