AI & ChatGPT searches , social queries for KAPREKAR NUMBER
Search references for KAPREKAR NUMBER. Phrases containing KAPREKAR NUMBER
See searches and references containing KAPREKAR NUMBER!
Search references for KAPREKAR NUMBER. Phrases containing KAPREKAR NUMBER
See searches and references containing KAPREKAR NUMBER!KAPREKAR 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
Indian recreational mathematician (1905–1986)
largely alone, Kaprekar discovered a number of results in number theory and described various properties of numbers. In addition to the Kaprekar's constant
D._R._Kaprekar
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
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
Natural number
= 7!, superior highly composite number 5041 = 712, centered octagonal number 5050 – triangular number, Kaprekar number, sum of first 100 integers 5051
5000_(number)
Natural number
23,1,0), to the Prime in the 23-aliquot tree. a Kaprekar number a lucky number a palindromic number in base ten the ninth repdigit the sum of the cubes
99_(number)
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
Natural number
example, 1234 / 9999 = 0.123412341234... . 9999 is a Kaprekar number. 9999 was the last possible line number in some older programming languages such as BASIC
9999_(number)
Natural number
graphs with two connected components. 999 = 33 × 37. It is a Kaprekar number and a Harshad number. In many video games, 999 is the maximum score that can be
900_(number)
Natural number
number 2221 – super-prime, happy number 2223 – Kaprekar number 2230 – sum of the totient function for the first 85 integers 2232 – decagonal number 2245
2000_(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
Leyland number: 66 + 66. Also a 3-smooth number. 94,249 = palindromic square: 3072 94,932 = Leyland number: 75 + 57 95,121 = Kaprekar number: 951212 =
90,000
Natural number
heptagonal number 4933 – super-prime 4941 – centered cube number 4943 – Sophie Germain prime, super-prime 4950 – triangular number, 12th Kaprekar number 4951
4000_(number)
Natural number
pronic number, a nontotient, and a Harshad number. 703 = 19 × 37. It is a hexagonal number, a Kaprekar number and the 37th triangular number. It is the
700_(number)
Natural number
seventy-four) is the natural number following 6173 and preceding 6175. It is a Kaprekar's Constant 6174 is a 7-smooth number, i.e., none of its prime factors
6174
Natural number
super-prime; largest four-digit prime 9988 – number of prime knots with 13 crossings 9999 – Kaprekar number, repdigit There are 112 prime numbers between
9000_(number)
Natural number
Chen prime. 38807 = number of non-equivalent ways of expressing 10,000,000 as the sum of two prime numbers 38962 = Kaprekar number 39299 = Integer connected
30,000
Natural number
significant number that is not the sum of the squares of distinct primes 17272 = weird number 17296 = amicable number with 18416 17344 = Kaprekar number 17389
10,000
Integer divisible by sum of its digits
uses all their digits, represent a Harshad number in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad"
Harshad_number
Natural number
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 be
297_(number)
Natural number
number 22222 = repdigit, Kaprekar number: 222222 = 493817284, 4938 + 17284 = 22222 22447 = cuban prime 22527 = Woodall number: 11 × 211 − 1 22621 = repunit
20,000
Natural number
written in binary, it is a non-repetitive Kaprekar number. It is also the sum of all the divisors of 100 and the number of week-month combinations in the Gregorian
217_(number)
Natural number
equal to 1 82,656 = Kaprekar number: 826562 = 6832014336; 68320 + 14336 = 82656 82,944 = 3-smooth number: 210 × 34 83,097 = Riordan number 83,160 = the 29th
80,000
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
Concept in number theory
integer. Arithmetic dynamics Dudeney number Factorion Happy number Kaprekar's constant Kaprekar number Meertens number Perfect digit-to-digit invariant Perfect
Narcissistic_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
Carmichael number 76084 = amicable number with 63020 76424 = tetranacci number 77778 = Kaprekar number 78163 = Friedman prime 78498 = the number of primes
70,000
Number that is its own Gödel number
b} . Arithmetic dynamics Dudeney number Factorion Happy number Kaprekar's constant Kaprekar number Narcissistic number Perfect digit-to-digit invariant
Meertens_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 Harshad number Keith number Kaprekar number Digit sum Persistence of a number Perfect digital invariant Happy number Perfect digit-to-digit invariant
List of recreational number theory topics
List_of_recreational_number_theory_topics
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
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
Number equal to the product of the sum and product of its digits
Arithmetic dynamics Dudeney number Factorion Happy number Kaprekar's constant Kaprekar number Meertens number Narcissistic number Perfect digit-to-digit invariant
Sum-product_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
Sequence in number theory
Arithmetic dynamics Factorion Happy number Kaprekar's constant Kaprekar number Meertens number Narcissistic number Perfect digit-to-digit invariant Perfect
Dudeney_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
Number whose square ends in the same digits
Arithmetic dynamics Kaprekar number p-adic number p-adic analysis Zero-divisor See Gérard Michon's article at "spherical number". Oxford English Dictionary
Automorphic_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
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
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
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
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
Natural number
800th prime number, twin prime with 6131 6143 – Thabit number 6144 – 3-smooth number (211×3) 6173 – Sophie Germain prime 6174 – Kaprekar's constant 6181
6000_(number)
List of terms created from a person's name
Hungarian dermatologist – Kaposi's sarcoma D. R. Kaprekar, Indian mathematician – Kaprekar constant, Kaprekar number Jacobus Kapteyn, Dutch astronomer – Kapteyn's
List_of_eponyms_(A–K)
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
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
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
Munchausen number
Dudeney number Factorion Happy number Kaprekar's constant Kaprekar number Meertens number Narcissistic number Perfect digital invariant Sum-product number van
Perfect digit-to-digit invariant
Perfect_digit-to-digit_invariant
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
Integer whose multiples are digit rotations
number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely-known cyclic number is
Cyclic_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
Type of natural number
described in 1959 by the Indian mathematician D. R. Kaprekar. Let n {\displaystyle n} be a natural number. We define the b {\displaystyle b} -self function
Self_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
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
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
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
Number equal to the sum of all or some of its divisors
In number theory, a semiperfect number or pseudoperfect number is a natural number n equal to the sum of all or some of its proper divisors. A semiperfect
Semiperfect_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
Positive integer whose divisors have a harmonic mean that is an integer
In mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic
Harmonic_divisor_number
Natural number
870,912 = 229 536,871,753 = Leyland number using 2 & 29 (229 + 292) 543,339,720 = Pell number 554,999,445 = a Kaprekar constant for digit length 9 in base
100,000,000
Integer whose representation contains every digit in its number base
In mathematics, a pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once. For
Pandigital_number
College in Pune, India
and sports administrator D. R. Kaprekar (1905–1986) — mathematician, discovered Kaprekar's routine and the Kaprekar number Sonali Kulkarni (born 1974) —
Fergusson_College
Odd number with specific properties
In mathematics, a Riesel number is an odd natural number k for which k × 2 n − 1 {\displaystyle k\times 2^{n}-1} is composite for all natural numbers
Riesel_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
Numbers with many divisors
highly composite number is a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive
Highly_composite_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
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
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
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
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
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
Concatenation of the first n prime numbers
In mathematics, a Smarandache–Wellin number is an integer that in a given base is the concatenation of the first n prime numbers written in that base.
Smarandache–Wellin_number
Number that has fewer digits than the number of digits in its prime factorization
In number theory, an extravagant number (also known as a wasteful number) is a natural number in a given number base that has fewer digits than the number
Extravagant_number
Number whose divisors add to a multiple of that number
perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number k, a number n is
Multiply_perfect_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
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
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
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 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
Number that is the sum of the factorials of its digits
Arithmetic dynamics Dudeney number Happy number Kaprekar's constant Kaprekar number Meertens number Narcissistic number Perfect digit-to-digit invariant
Factorion
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
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
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
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
Hardy–Ramanujan number, 1729 Kaprekar's constant, 6174 Eddington number, ~1080 Googol, 10100 Shannon number Centillion, 10303 Skewes's number Googolplex,
List_of_numbers
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
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)
Number that is the result of operation on its own digits
A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination
Friedman_number
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
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
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
Integer of the form 3 × 2^n – 1 for non-negative n
In number theory, a Thabit number, Thâbit ibn Qurra number, or 321 number is an integer of the form 3 ⋅ 2 n − 1 {\displaystyle 3\cdot 2^{n}-1} for a non-negative
Thabit_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
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
Numbers that contain only the digit 1
164–167 Francis 1988, pp. 240–246 Kaprekar 1938a, 1938b, Gunjikar & Kaprekar 1939 Weisstein, Eric W. "Demlo Number". MathWorld. Beiler, Albert H. (2013)
Repunit
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
Mathematical concept in prime numbers
power. In particular, a number that has two distinct representations as a sum of two squares is composite. Every idoneal number generates a set containing
Idoneal_number
Number sequence 3,0,2,3,2,5,5,7,10,...
} The number of different maximal independent sets in an n-vertex cycle graph is counted by the nth Perrin number for n ≥ 2. The solution
Perrin_number
Type of positive integer
In number theory, a positive integer k is said to be an Erdős–Woods number if it has the following property: there exists a positive integer a such that
Erdős–Woods_number
Number whose sums of distinct divisors represent all smaller numbers
In number theory, a practical number or panarithmic number is a positive integer n {\displaystyle n} such that all smaller positive integers can be represented
Practical_number
KAPREKAR NUMBER
KAPREKAR NUMBER
KAPREKAR NUMBER
KAPREKAR NUMBER
KAPREKAR NUMBER
KAPREKAR NUMBER
KAPREKAR NUMBER
KAPREKAR NUMBER
KAPREKAR NUMBER