 ## Filters Tab ### Overview

This is the second tab in the Main window, and is used for setting the optional filters used for the analysis.

### How to Invoke

Click the "Filters" tab in the Main Window.

### Basic Procedure

1. Choose the Assertion filters (optional)
2. Choose the Rejection filters (optional)
3. Choose the Limitation Deviation
4. Choose the Limitation filters (optional)

### Window Controls

#### "Assertion" Filters

All filters are optional, and are a way of helping you 'fine tune' Lotto Sorcerer's suggestion process. Checking any of the Assertion Filters means that the attribute you choose must be in the suggestions produced. Here are the descriptions of the specific filters and their attributes:

• "Adjacent 2" : This filter requires that each suggestion produced must have two, and only two numbers, that are 'back-to-back'. For example, the suggestion set of '02-03-08-19-31' would be allowed, because the '02' and the '03' are adjacent to each other.
• "Repeat 1" : This filter requires that each suggestion produced contains one number, and only one number, that was chosen in the previous drawing.
• "Prime 1+" : This filter requires that each suggestion produced contains at least one prime number.
• "Factor of 3" : This filter requires that each suggestion produced contains at least one number that is a factor of three.
• "Triangular Numbers 1+" : This filter requires that each suggestion produced contains at least one number that is a 'triangular number'. A triangular number counts the objects that can form an equilateral triangle. The sequence of triangular numbers, up to 99, starting at the 0th triangular number, is: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91.
• "Ulam Numbers 1+" : This filter requires that each selection produced contains at least on number that is an 'Ulam number'. An Ulam number is a member of an integer sequence devised by and named after Stanislaw Ulam, who introduced it in 1964. The standard Ulam sequence (the (1, 2)-Ulam sequence) starts with U1 = 1 and U2 = 2. Then for n > 2, Un is defined to be the smallest integer that is the sum of two distinct earlier terms in exactly one way. The sequence of Ulam numbers (up to 99) is: 1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, 36, 38, 47, 48, 53, 57, 62, 69, 72, 77, 82, 87, 97, 99.
• "Square Numbers 1+": This filter requires that each suggestion produced contains at least one number that is a "square number". A square number is an integer that is the square of an integer. The sequence of square numbers, up to 99, is: 1, 4, 9, 16, 25, 36, 49, 64, 81.
• "Pentagonal Numbers 1+: This filter requires that each suggestion produced contains at least one number that is a "pentagonal number". A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The sequence of pentagonal numbers, up to 99, is: 1, 5, 12, 22, 35, 51, 70, 92.
• "Fibonacci Numbers 1+": This filter requires that each suggestion produced contains at least one number that is a "Fibonacci number". A Fibonacci number is characterized by the fact that every number after the first two is the sum of the two preceding ones. The sequence of Fibonacci numbers, up to 99, is: 0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.
• "Padovan Sequence 1+": This filter requires that each suggestion produced contains at least one number that is a member of the "Padovan sequence", named after Richard Padovan. The Padovan sequence, up to 99, is: 1, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86.
• "Semi Perfect Numbers 1+": This filter requires that each suggestion produced contains at least one number that is a "semi perfect number". A semi perfect number is a natural number n that is equal to the sum of all or some of its proper divisors. The sequence of semi perfect numbers, up to 99, is: 6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 84, 88, 90, 96.
• "Semi Prime Numbers 1+": This filter requires that each suggestion produced contains at least one number that is a "semi prime number". A semi prime number is a natural number that is the product of two (not necessarily distinct) prime numbers. The sequence of semi prime numbers, up to 99, is: 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95.
• "Perfect Numbers 1+": This filter requires that each suggestion produced contains at least one number that is a "perfect number". A perfect number is a positive integer that is equal to the sum of its proper positive divisors. The sequence of perfect numbers up to 99, is: 2, 3, 4, 6, 8, 10, 12, 15, 18, 21, 24, 26, 32, 39, 42, 60, 65, 72, 84, 96.
• "Deficient Numbers 1+": This filter requires that each suggestion produced contains at least one number that is a "deficient number". A deficient number is a number in which the sum of all the divisors of the number (n)<2 is less than twice the value of the number n. The sequence of deficient numbers up to 99, is: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86.
• "Composite Numbers 1+": This filter requires that each suggestion produced contains at least one number that is a "composite number". A composite number is a positive integer that can be formed by multiplying together two smaller positive integers. The sequence of composite numbers, up to 99, is: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99.
• "Abundant Numbers 1+": This filter requires that each suggestion produced contains at least one number that is an "abundant number". An abundant number is a number for which the sum of its proper divisors is greater than the number itself. The sequence of abundant numbers, up to 99, is: 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96.
• "Calculations" : This filter is actually a collection of ten separate assertion filters, each filter a calculated value. Clicking the 'Set' button will invoke the Set Assertive Calculations window. To set any of the assertive calculation filters, check the desired filter and enter the appropriate values in the 'from' and 'to' filters. Also, the "Calculations" filter in the Assertion Filters section of the Projection Parameters in the Main Window must be checked. When any of the Assertive Calculation filters is active, only those suggestions that meet the entered criteria will be allowed.

#### "Rejection" Filters

These filters reject potential suggestions outright:

• "Prior drawn" numbers: if checked, Lotto Sorcerer will not suggest numbers that have previously been drawn.
• "Adjacent 2+" numbers: this rejects suggestions that are back-to-back (for example, the suggestion '02-08-09-13-22' would be rejected, because the numbers '08' and '09' are adjacent.
• "Adjacent 3+" numbers: this rejects suggestions that have three numbers that are adjacent.
• "Adjacent 4+" numbers: this rejects suggestions that have four numbers that are adjacent.
• "Skewed Hot" : this rejects suggestions that are all hot. This filter is not available if you use the Pool Temperature engine, because this engine might decide that you should use all hot numbers.
• "Skewed Medium" : this rejects suggestions that are all medium in 'temperature'. This filter is not available if you use the Pool Temperature engine, because this engine might decide that you should use all medium numbers.
• "Skewed Cold" : this rejects suggestions that are all cold numbers. This filter is not available if you use the Pool Temperature engine, because this engine might decide that you should use all cold numbers.
• "Skewed Even" : this rejects suggestions that are all even numbers. This filter is not available if you use the Parity engine, because this engine might decide that you should use all even numbers.
• "Skewed Odd" : this rejects suggestions that are all odd numbers. This filter is not available if you use the Parity engine, because this engine might decide that you should use all odd numbers.
• "Skewed High" : this rejects suggestions that are all high numbers. This filter is not available if you use the Distribution engine, because this engine might decide that you should use all high numbers.
• "Skewed Middle" : this rejects suggestions that are all middle numbers. This filter is not available if you use the Distribution engine, because this engine might decide that you should use all middle numbers.
• "Skewed Low" : this rejects suggestions that are all low numbers. This filter is not available if you use the Distribution engine, because this engine might decide that you should use all low numbers.
• "Repeat 1+ " : this filter rejects suggestions that contains one or more numbers that are in the previous drawing. This does not consider bonus numbers.
• "Repeat 2+ " : this filter rejects suggestions that contains two or more numbers this are in the previous drawing. This does not consider bonus numbers.
• "User Defined" : The filter allows the user to enter a comma-delimited string of numbers which will be disallowed from the suggestions. Clicking the Set button will invoke the Set Rejectors window.

#### "Limitation Deviation"

This selection affects the range of the Limitation filters. The Limitation filters keep all suggestions within a certain statistical range, but what range? This control lets you select that range. The range is defined as standard deviations. You can select from 1 standard deviation ( "sigma" ) to 3 standard deviations. You can set the "from" and the "to" values independently from each other, but not for each Limitation Filter.

#### "Limitation" Filters

These powerful filters, if selected, will pass only that suggestions that are statistically within the range of the average of drawings as chosen in the "Sampling Size" dropdown. And the range is decided by the Limitation Deviation selection.

For example, suppose you have selected both limitation deviation settings to 3, and the median limitation filter checked. When Lotto Sorcerer calculates a suggested set of numbers to play, it will calculate its median; then it will determine the average of the median of the past drawings. If the suggested drawing's median is within 2 standard deviations of the average of the past numbers, it will be passed as a valid number set to play.

Tip: if you use the Lotto Seer function (menu item 'Tools > Lotto Seer'), you can view how often prior drawings exceed any of the standard deviations by viewing the line chart for that particular statistical function. For example, this shows the Median values: As you can see, the right of the chart shows the six standard deviation lines, three above the Average (+1 sigma, +2 sigma, and +3 sigma); and three below the Average (-1 sigma, -2 sigma, and -3 sigma). The chart itself shows that no drawing has ever gone below -3 sigma nor above +3 sigma . So setting the Limitation Deviation radio buttons at -3 sigma and +3 sigma would ensure no suggestion will appear that would exceed those values.

These Limitation Filters are all statistical functions, and are described in the Glossary section of the Lotto Sorcerer v9 User's Guide.

#### "Notes" text box

This box lets you save a short note for this lottery's filter settings. You are limited to 254 characters.

#### "Print" Button

This prints out the Projection Parameters and Filters settings.