The difference between the consecutive terms in a sequence of shifted times tables tells me what times table it is. Ex: 4,6,8,10…,112,114,116… The difference between the consecutive terms is 2. This means its a times table of 2. Ex: 3,5,7,9…113,115,117…. The difference between the consecutive terms is also 2 but it is shifted up by 1 and shifted down by 1. This means that this table is still counting by twos meaning its a table of multiples of 2.
If all the numbers are odd then the table is counting by an even number. Ex:(6,[3,3])
If all the numbers are even then it is also counting by even numbers. Ex:(8,[4,4])
If it is a mixture of even and odd numbers, then the table is counting by an odd number.
If all the digits are identical then it will result in a table counting by even numbers. Ex: (6,[3,3]) (10,[5,5])
If the difference between the two numbers is prime then the table is shifted either up or down by 1.
If the difference between the two numbers is odd and composite then it is shifted up and down by composite and prime numbers. If it is even, then it is shifted by prime numbers.
To work the table you first find the difference between the first and second numbers. Then you find the difference between the first and the table interval it is counting up by. Then multiply the table number by three and subtract it from the second number to get the shifted down number.