collatz {FunWithNumbers}

Test the Collatz Conjecture. ~~

Description

This function calculates the Collatz (aka Hailstone) sequence based on the selected starting integer.

Usage

collatz(x, div=2, mul=3, add= 1, maxKnown=1, maxiter = 1000)

Arguments

x

The integer, or bigz integer to start with.

div

The integer to divide by. Default is 2 per the original Collatz formula.

mul

The integer to multiply by. Default is 3 per the original Collatz formula.

add

The integer to add after multiply. Default is 1 per the original Collatz formula.

maxKnown

An integer to use as a "shortcut" if you know that said value converges. This allows the user to avoid repeating previous calculations. Default value is 1, i.e. no previous knowledge of converging numbers.

maxiter

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

Details

The Collatz sequence follows simple rules: If the current number is even, divide it by two; else if it is odd, multiply it by three and add one. Convergence occurs in < 200 cycles for initial values < 10 million or so. Note: a serious Collatz generator would memoize previous successful sequences, thus greatly reducing the calculation time required to test new numbers. This function is provided "for amusement only."

Value

A vector of bigz integers representing the sequence, either to convergence or as limited by maxiter

Author(s)

Carl Witthoft, [e-mail]

Examples

(collatz(20))
# 20 10 5  16 8  4  2 
(collatz(234568))
# [1] 234568 117284 58642  29321  87964  43982  21991  65974  32987  98962
#  49481  148444 74222  37111 
# [15] 111334 55667 167002 83501 250504 125252 62626 31313 93940 46970 23485
# 70456 35228 17614 
# [29] 8807  26422 13211 39634 19817 59452 29726 14863 44590 22295 66886
# 33443 100330 50165 
# [43] 150496 75248 37624 18812 9406  4703  14110 7055  21166 10583 
#31750 15875 47626 23813 
# [57] 71440 35720 17860 8930  4465  13396 6698  3349  10048 5024  
#  2512  1256  628  314  
# [71] 157  472  236  118  59   178  89   268  134  67   202  101  304  152  
# [85] 76   38   19   58   29   88   44   22   11   34   17   52   26   13  
# [99] 40   20   10   5   16   8   4   2