Dattatreya ramchandra kaprekar 19051986 was an indian recreational mathematician who described several classes of natural numbers including the kaprekar, harshad and self numbers and discovered the kaprekar constant, named after him. Symmetry free fulltext on some formulas for kaprekar. Write a program in java to input a number and check whether it is a kaprekar number or not note. The decimal n kaprekar numbers are defined and are shown to be in oneone correspondence with the unitary divisors of 10n 1. The decimal nkaprekar numbers are defined and are shown to be in oneone correspondence with the unitary divisors of 10n 1. Media in category kaprekar s constant the following 5 files are in this category, out of 5 total. The mystery and music of kaprekar constant 6174 renaissance. The concept of kaprekar numbers is not limited to base 10 i. The main idea is that every number that our program takes sooner or later the result has to be 6174 following the kaprekars routine. Naranan sixty years after its discovery and twenty years after kaprekars death, kaprekar constant 6174 continues to fascinate amateur mathematicians, mathematics teachers and devotees of recreational and experimental mathematics. Arrange the digits in descending and then in ascending order to get two fourdigit numbers, adding leading zeros if. Or, rather, then you can go ahead and see what i did below. Kaprekar s constant using c language this project was based on the kaprekar s constant.
First gotcha is the second part of the split numbers must be positive no zeros. Square it and add the right n digits to the left n or n1 digits. There are some wonderful attempts to convert the digits of mathematical constant pi to musical sequence check michael john blake a musical interpretation of pi, and lucy kaplansky song about pi. Pdf kaprekar constant 6174 continues to fascinate amateur mathematicians, mathematics teachers and devotees of recreational and experimental mathematics find, read and cite all the research. If the sum of the two pieces is equal to the number, then n is a. The number 6174 is the only unchanged mysterious number discovered by kaprekars operation. We have converted the number into a sequence of characters, so that we can do the next thing, which is call the list. In this note, a new scheme for generating all the nkaprekar numbers less than or equal to a specified value is obtained. All natural numbers less than 10,000 except some with same digits can be reduced to 6174 in the followi. Talentsprint aptitude prep channel is designed to help aspirants get ready for various competitive exams including bank, ssc, railways, insurance, campus recruitment and. Generate and show all kaprekar numbers less than 10,000. There are three series for 5digit numbers 74943 62964 71973 83952 repeat 63954 61974 82962 75933 repeat 53955 59994 repeat series for 6digit. However, the square of some n digit numbers is only 2n 1. There is one kaprekar constant for 3digit numbers 495.
Kaprekar constant, or 6174, is a constant that arises when we take a 4digit integer, form the largest and smallest numbers from its digits, and then subtract these two numbers. In mathematics, a natural number in a given number base is a kaprekar number if the representation of its square in that base can be split into two parts, where the second part has digits, that add up to the original number. If you are as amazed as i am and want some additional information about the mathematics involved in the algorithm, then you can click on one of the links below. To find out all possibilities, you only have a finite computation to do but a computer may help. Go read about kaprekar numbers and then try to build your own kaprekar number generator. Mar 10, 2017 talentsprint aptitude prep channel is designed to help aspirants get ready for various competitive exams including bank, ssc, railways, insurance, campus recruitment and other govt exams. The kaprekar method is very easy to use and is the following. The decimal nkaprekar numbers are defined and are shown to be in oneone correspondence with the unitary divisors of 10 n 1. In this note, a new scheme for generating all the n kaprekar numbers less than or equal to a specified value is obtained.
Kaprekar process accessed in goo gle thr ough kapr ekar c onstant 6174. Series for 4digit numbers there is one kaprekar constant for 4digit numbers 6174. Take a look at the code, and then well walk through this one, introducing a new type of function called a generator function. Given a number, the task is to check if it is kaprekar number or not. In fact, 9, 55 and 95121 are 1 kaprekar, 2 kaprekar and 5 kaprekar numbers, respectively. L, generating l and l such that l is the digits of l in ascending order and l is the digits in descending order and subtracting l l always converge to the kaprekar constant of 6174. Kaprekars constant as a fixed point of iterative function. Here is a common problem in elementary school arithmetic. This algorithm is credited to the indian mathematician d. If t b, n x x, then x is called a badic ndigit kaprekar constant.
The number 6174 is the only unchanged mysterious number discovered by kaprekar s operation. Why does the kaprekar process of taking a 4 digit number. Arrange the digits in descending and then in ascending order to get two fourdigit numbers, adding leading zeros if necessary. On 2adic kaprekar constants and 2digit kaprekar distances. Apr 29, 2014 the major scale consists of 7 notes from any chromatic scale and we have already seen that the kaprekar constant can be reached at the most 7 iterations. But avoid asking for help, clarification, or responding to other answers. Therefore b 2 and p is a mersenne prime number, since any 2adic kaprekar constant is the product of two suitable mersenne numbers by theorem 0. Al nicholson, nick jefferson, mike westergaard, david jackson, bill jefferson, dorie jackson. Pdf a variant of kaprekar iteration and kaprekar constant. The decimal n kaprekar numbers are defined and are shown to be in oneone correspondence with the unitary divisors of 10 n 1. A positive whole number n that has d number of digits is squared and split into two pieces, a righthand piece that has d digits and a lefthand piece that has remaining d or d1 digits. The series of kaprekar numbers is known as a006886, and begins as 1,9,45,55. A student talked about kaprekars constant 6174 during their my favorite presentation.
How to prove kaprekars constant 6174 in layman terms. Kaprekars constant using c language this project was based on the kaprekars constant. Take any fourdigit number, using at least two different digits. Iannucci the university of the virgin islands 2 john brewers bay st. Kaprekar was an indian mathematician who came up with this beautiful result from number theory in 1946. The major scale consists of 7 notes from any chromatic scale and we have already seen that the kaprekar constant can be reached at the most 7 iterations. Rearranging to form the largest and smallest with these digits, we. Watch this video if youre still unclear on how kaprekars routine works. If the resultant sum is k, then k is called a kaprekar number. In particular, this establishes the correctness of an algorithm for generating the kaprekar numbers. Nm is the number of seeds requiring m iterations to the e nd.
Is kaprekars constant useful for anything or is it just a. Continuing with this process of forming and subtracting, we will always arrive at the number 6174. Then, we define the kaprekar transformation t b, n x. A kaprekar number is a number whose square when divided into two parts and such that sum of parts is equal to the original number and none of the parts has value 0. Program to check for kaprekar number guide for school.
Every kaprekar number with 2n digits is the square of a number with n digits, so to find all of the kaprekar numbers below 1014, inspect the squares of all numbers below 107. Solarwinds database performance monitor dpa helps application engineers, including devops teams, see exactly how new code impacts database workload and query response, even before its deployed. This number is special as we always get this number when following steps are followed for any four digit number such that all digits of number are not same, i. B be the badic ndigit integer obtained by rearranging the numbers of all digits of x in descending resp. The major scale consists of 7 notes from any chromatic scale and we have already seen that the kaprekar constant can be reached at the most 7. A kaprekar number is a sociable kaprekar number with, and a amicable kaprekar number is a sociable kaprekar number with. Wolframs mathworld describes kaprekar numbers like this consider an ndigit number k. In particular, this establishes the correctness of an algorithm.
It has always been a fascinating theorem, easily understood but hard to prove for amateurs, a lesser fermats last theorem. Challenge in the language of your choice, write a script to find the first 8 kaprekar numbers. Boerderij official bootleg kaprekars constant boerderij dvd official bootleg boxset. Kaprekar numbers below 0 1 1 2 9 3 45 4 55 5 99 6 297 7 703 8 999 9 2223 10 2728 11 4879. Back in 1989 i read about this series in a mathematical journal, and was fascinated the moment i read about it. Discover the mystery behind the 6174 loop by using any four digit number. When p is 9, this code constructs the value 9 2, or 81. The fixed point, 6174, is sometimes called kaprekars constant. A modified kaprekar number is a positive whole number n with d digits, such that when we split its square into two pieces a right hand piece r with d digits and a left hand piece l that contains the remaining d or d. There are three series for 5digit numbers 74943 62964 71973 83952 repeat 63954 61974 82962 75933 repeat 53955 59994 repeat. Some properties of the kaprekar numbers and a means of generation. For those who knows kaprekars constant may skip 1st paragraph. Some properties of the kaprekar numbers and a means of. Despite having no formal postgraduate training and working as a schoolteacher, he published extensively and.
Weisstein world of mathematics kaprekar number, kaprekar routine, 196algorithm. Then we use the str function to change the integer 81 into the string 81. It should be generalized to an arbitrary length and an arbitrary base, then if it is true that there are a finite number of fixed points, the conjecture that it holds for an arbitrary base give two kaprekar functions of the base and length less th. In fact, 9, 55 and 95121 are 1kaprekar, 2kaprekar and 5kaprekar numbers, respectively. Optionally, count and report the count of how many kaprekar numbers are less than 1,000,000. Sep 29, 2014 a student talked about kaprekars constant 6174 during their my favorite presentation. Steps from wikipedia take any fourdigit number, using at least two different digits. The main idea is that every number that our program takes sooner or later the result has to be 6174 following the kaprekar s routine. Kaprekar steps code challenge matlab matlab programming. In this section, we shall give a brief survey of some results of young and prove theorem 0. How to prove kaprekars constant 6174 in layman terms quora.
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