***Collatz_Sequences (3*N+1) in Console Example Demo for TCL V2 ***
 
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<<TOC>>

***Preface*** 
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***Introduction***
Here are TCL calculations on  the Collatz Sequences. 
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The collatz_sequence proc returns the collatz_sequence from positive integers. This program can easily generate an endless loop. The iteration number is a stop or limit to iteration. By custom, the end of collatz_sequence is 1 or start of repetition.
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if $N even, return { $N / 2 }.  If $N odd,  return (3*$N+1). Continue the collatz_sequence until returned item is 1 or start of repetition.
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***References:***
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   * Wikipedia search engine < Collatz Sequences  >
   * Wikipedia search engine < Lothar Collatz Sequences >
   * Wikipedia search engine <  Programming Examples  >
   * Google search engine < vaporware   >
   * Google search engine < Collatz_Sequences  >
   * Book >> How to Prove The Collatz Conjecture Paperback,  2005, by Danny Fleming 
   * Ultimate Challenge: the 3x + 1 problem: edited by Jeffrey Lagarias, 
   * [One Liners Programs Pie in the Sky] 
   * [One Liners] 
   * One Liners Programs Compendium [https://wiki.tcl-lang.org/page/One+Liners+Programs+Compendium++and+TCL+demo+examples+calculations%2C+numerical+analysis]
   *        WIKI BOOKS,  Programming_Examples pdf
   *        WIKI BOOKS, Tcl_Programming_Introduction pdf
   * google search engine <  Collatz Conjecture >
   * [switch] 
   * [Tcl Tutorial Lesson 6] 
   * [Math Sugar] [Richard Suchenwirth] [RS] 
   * tmml.sourceforge.net/doc/tcllib [http://tmml.sourceforge.net/doc/tcllib/interpolate.html]
   * rosettacode.org/wiki/Even_or_odd [https://rosettacode.org/wiki/Even_or_odd#Tcl]
   * en.wikipedia.org/wiki/Collatz_conjecture
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***Screenshots Section***
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****figure 1. Screenshot, Collatz_Sequences_(3*N+1) _screenshot ****
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[Collatz_Sequences_(3*N+1) _screenshot]
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***Testcases Section***  

In planning any software, it is advisable to gather a number of testcases to check the results of the program.

**** Testcase 1, Partial Collatz_Sequences  ****
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%| table, Partial Collatz_Sequences  |  | printed in|TCL format |% 
%| number | iteration |partial Collatz_Sequences  |comment, if any|% 
&| 3 | 5   | 3 10 5 16 8 4 2 1| |&
&| 4 | 5   | 4 2 1| |&
&| 5 | 5   | 5 16 8 4 2 1| |&
&| 6 | 5   | 6 3 10 5 16 8 4 2| |&
&| 7 | 5   | 7 22 11 34 17 52 26 13 40| |&
&| 8 | 5   | 8 4 2 1| |&
&| 9 | 5   | 9 28 14 7 22 11 34 17 52| |&
&| 10 | 5   | 10 5 16 8 4 2 1| |&
&| 11 | 5   | 11 34 17 52 26 13 40 20| |&
&| 12 | 5   | 12 6 3 10 5 16 8 4| |&
&| 13 | 5   | 13 40 20 10 5 16 8| |&
&| 14 | 5   | 14 7 22 11 34 17 52 26 13 40| |&
&| 15 | 5   | 15 46 23 70 35 106 53 160 80| |&
&| 16 | 5   | 16 8 4 2 1| |&
&| 17 | 5   | 17 52 26 13 40 20 10| |&
&| 18 | 5   | 18 9 28 14 7 22 11 34 17 52| |&
&| 19 | 5   | 19 58 29 88 44 22 11 34| |&
&| 20 | 5   | 20 10 5 16 8 4 2| |&
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****Appendix TCL programs and scripts ****

**** Pretty Print Version*** 

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======
        # pretty print from autoindent and ased editor
        # Collatz_Sequences (3*N+1) in Console Example Demo for TCL V2
        # Console program example demo
        # written on Windows 10 on  TCL
        # working under TCL version 8.6
        # gold on TCL Club , 11sep2021
        package require Tk
        package require math::numtheory
        package require math::constants
        package require math::trig
        package require math
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory math::trig math::constants }
        set tclprecision 17
        ;# logic tests for even,  odd, positive, negative,  conditions of positive  numbers
        ;# uses logic inside expr , if positive return 1, if not positive return 0
        proc isPositive x {return [ expr {$x>0}]}
        ;# Richard Suchenwirth RS idea  in Math Sugar
        ;# uses logic inside expr, if negative return 1, if not negative return 0
        proc isNegative  x { return [ expr {$x<0}]}
        ;# Richard Suchenwirth RS idea from wiki: Math Sugar
        ;# idea by Michael Barth
        ;# No error traps or safety nets here for negative and real numbers.
        ;# conditional proc  IsOdd,  if N odd, return 1, if N not odd, return 0.
        proc IsOdd { N }  { return [ expr {$N % 2} ] }
        ;# Usage
        IsOdd 5  ;# returns 1
        ;# conditional proc IsEven,  if N even,  return 1. If N not even return 0.
        proc IsEven { N }  { return [ expr { ( $N + 1 ) % 2} ] }
        IsEven 4 ;# returns 1
        ;#
        ;# Results: collatz_sequence
        ;#
        ;# Return the collatz_sequence from positive integer
        ;#
        ;# Arguments:
        ;#    number first value is number
        ;#    iteration second value is iteration
        ;#
        ;#
        ;# Note: This program can easily generate an endless loop.
        ;#        iteration number is a stop or limit to iteration
        ;# By custom, the end of collatz_sequence is 1 or start of repetition
        proc collatz_sequence {number iteration} {
            set sequence  [ list ]
            set count 0
            set val $number
            set skip 0
            lappend sequence $val
            while {$count < $iteration} {
                if { $val == $skip   } { lappend sequence  1 ; break }
                
                if { [ IsEven $val ] } { set val [ expr { $val / 2 } ] ; lappend sequence $val  }
                if { [ IsOdd $val ] } { set val [ expr { (3 *  $val ) + 1 } ]; lappend sequence $val   }
                incr count
                if { $count == $iteration   } { break }
                set skip 2
            }
            return $sequence
        }
        console show
        puts "  Console wrapper for solution proc"
        puts "  ***************************"
        puts "  ***************************"
        puts "collatz_sequence 31 15 collatz_sequence [collatz_sequence 31 15]"
        puts "collatz_sequence 11 15 collatz_sequence [collatz_sequence 11 15]"
        puts "collatz_sequence 10 15 collatz_sequence [collatz_sequence 10 15]"
        puts "collatz_sequence 9 15 collatz_sequence [collatz_sequence 9 15]"
        puts "collatz_sequence 8 15 collatz_sequence [collatz_sequence 8 15]"
        puts "collatz_sequence 7 15 collatz_sequence [collatz_sequence 7 15]"
        puts "collatz_sequence 6 15 collatz_sequence [collatz_sequence 6 15]"
        puts "collatz_sequence 5 15 collatz_sequence [collatz_sequence 5 15]"
        puts "collatz_sequence 4 15 collatz_sequence [collatz_sequence 4 15]"
        puts "collatz_sequence 3 15 collatz_sequence [collatz_sequence 3 15]"
        proc table_format_out  n {
            set sum 0
            # initial  level
            set count 1
            puts "%| table|  | printed in|TCL format |% "
            puts "%| number | iteration |partial Collatz_Sequences  |comment, if any|% "
            # adapted proc from <RS>
            # printout in TCL WIKI format table
            for { set i 1 } { $i <= $n } { incr i } {
                incr count
                puts "&| $count | 5   | [ collatz_sequence $count 5 ]| |&"
                incr sum $i
            }
            return $sum
        }
        table_format_out 31
        # following dresses up console output to easy eye
        # end of working deck
        # add cosmetics below to bottom of file
        console eval {.console config -bg palegreen}
        console eval {.console config -font {fixed 20 bold}}
        console eval {wm geometry . 40x20}
        console eval {wm title . " Report for Collatz_Sequences (3*N+1) Calculator V2  "}
        console eval {. configure -background orange -highlightcolor brown -relief raised -border 30}         
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Please include your wiki MONIKER and date in your comment with the same courtesy that I will give you. Thanks, [gold] 12Aug2020 

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