Conjecture proof scripts

collatz-graph.sh

#!/usr/bin/env zsh

zmodload zsh/mathfunc
setopt extended_glob
BN="${${0##*/}%%.*}"
{
NC=(1)
echo "strict digraph collatz {"
for n in {2..$1}; do 
  if [ ! ${NC[(r)$n]} ]; then
    echo -n "$n "
    NC=($n;$NC)
  else
    continue
  fi 
  while [ $n != 1 ]; do
    if [ $[$n%2] = 0 ]; then
      n=$[$n/2]
    else 
      n=$[(3*$n)+1]
    fi
    if [ ! ${NC[(r)$n]} ]; then
      echo -n "-> $n "
      NC=($n;$NC)
    else
      echo "-> $n;"
      break
    fi
  done
done
echo 
for nc in $NC; do
  if [ ! $[$nc%2] = 0 ]; then
    k=$[log2($nc+1)]
    if [ ! ${k#*.} ]; then
      c="$[ceil($k)]"
      if [ $[${c%.*}%2] = 0 ]; then
        S="doublecircle"
      else
        S="circle"
      fi
    else
      S="ellipse"
    fi
  else
    k=$[log2($nc+1)/log2(3)]
    if [ ! ${k##*.(0##??)#} ]; then
      S="square"
    else
      S="rectangle"
    fi
  fi
  echo "$nc [shape=$S];"
done
echo "}"
} > $BN.dot

dot -Tpdf:cairo $BN.dot > $BN.pdf

collatz-length.sh

#!/bin/zsh

# Sort the first 100 natural numbers by the lenght of the Collatz sequence that they generate.

function collatz () { setopt extended_glob; n=${1##0#}; echo -n "$n "; [[ $n == 1 ]] && return; n=${$(($1.0/2.0))%%.}; [ $(grep -F . <<< $n) ] && n=$((($1*3)+1)); collatz $n; n=0 }
for n in {001..100}; do echo -n "collatz($n): "; awk -F' ' '{print $0" #"NF}' <<< ${$(collatz $n)##0#}; done | sort -n -k2.1 -t\# | awk -F'[()]' '{gsub(/^0*/,"",$2); printf $2" "}'
# for N in {002..100}; do set -A COLLATZ $(collatz $N); float -F 10 Q=$(($(((${#$(([#2]$N))}-2)-1)).0/$((${#COLLATZ}-1)).0)); echo "$N: $Q"; done | sort -k 2.1 -t .

# for n in {1..1000}; do for i in $(eval printf '%s\\n' $(printf '{0,1}%.s' {1..3}) | grep -v 11); do while [ $n != 1 ]; do echo -n $[$n%2]; [ $[$n%2] = 0 ] && n=$[$n/2] || n=$[3*$n+1]; done | sed 's/$/1000/;s/.../&'\\$'\n'/g | sed -n '$!p' | grep -c $i; done; echo; done | rs -T | fold -w20 | awk '{S1+=$1;S2+=$2;S3+=$3;S4+=$4;S5+=$5} END{print S1" "S2" "S3" "S4" "S5}'
# for n in {1..10}; do eval printf '%s\\n' $(printf '{0,1}%.s' {1..$n}) | grep -v 11 | wc -l; done

collatz-lsb.sh

#!/bin/zsh

# http://vixra.org/pdf/1005.0025v1.pdf

setopt extended_glob; N=$1
while [ ${N%%10#} ]; do
        echo $N; N=$(echo {i,o}base=2\; \
        "$N*11+${N/${N%%10#}}" | bc); done