kaprekar {FunWithNumbers}

Calculate the Kaprekar Sequence. ~~

Description

This function calculates the Kaprekar sequence based on the selected starting integer.

Usage

kaprekar(x, base = 10, addZeros = FALSE, maxiter = 1000)

Arguments

x

The integer, bigz, or character string representing the integer to start with.

base

The base of x. Bases 2 through 36 are supported.

addZeros

If a calculated term has fewer digits than the original x, addZeros, when TRUE, prepends zeros to maintain the number of digits.

maxiter

A "safety switch" to avoid possible lengthy runtimes (when starting with very very large numbers), terminating the function prior to convergence.

Details

The kaprekar sequence follows simple rules: In the given base, sort the digits in ascending order. Reverse that order, and calculate the absolute value of the difference. Feed that result back to the algorithm. In some cases, the sequence will converge to a value which produces itself. In others, the sequence may fall into a repeating cycle.

Value

A list, containing: theseq: a vector of bigz integers representing the sequence, either to convergence or as limited by maxiter converged: a logical value indicating whether the sequence reached a value or a cycle. This is useful primarily if maxiter is reached and it's not immediately clear whether convergence occurred.

Author(s)

Carl Witthoft, [e-mail]

References

https://en.wikipedia.org/wiki/Kaprekar's_routine

Examples

(kaprekar(2031))
# $theseq
# Big Integer ('bigz') object of length 5:
# [1] 2031 3087 8352 6174 6174
# $converged
# [1] TRUE

(kaprekar('0099'))
# $theseq
# Big Integer ('bigz') object of length 3:
# [1] 99 0  0 
# $converged
# [1] TRUE

 (kaprekar('0099', addZeros = TRUE) )
# $theseq
# Big Integer ('bigz') object of length 6:
# [1] 99   9801 9621 8352 6174 6174
# $converged
# [1] TRUE