Pseudo random sequence

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A pseudo random number is a false-random number - a number that may appear to be random, but is not actually random.

The term "pseudo" is from the Greek for false.

Here is a simple way to create a series of pseudo random digits from 0 to 9.

Pick a prime number larger than 10, say 17 (the increment).
Pick a starting number from the range such as 0 to 9, say 5. This is the seed value (initial random number).

The method to get the next random value r from the previous random value r is the following.

(r + increment) mod 10 -> r

The seed is the initial value for r. Here is the sequence of 10 random digits from 0 to 9.

5+17 = 22 -> 2 2+17 = 19 -> 9 9+17 = 26 -> 6 6+17 = 23 -> 3 3+17 = 20 -> 0 0+17 = 17 -> 7 7+17 = 24 -> 4 4+17 = 21 -> 1 1+17 = 18 -> 8 8+17 = 25 -> 5

At this point, the pseudo random sequence repeats.

If you pick a large prime number, and a short sequence, the sequence "appears" to be random. At least, it appears random until enough of the sequence is known and the pattern emerges.

Here is the Python code.

increment1 = 17
seed1 = 5
d1 = seed1
len1 = 100
for pos1 in range(1,len1+1):
	d1 = (d1 + increment1) % 10
	print(" {0:d}".format(d1),end="")
	if d1 == seed1:
		print("")

Here is the output of the Python code.

 2 9 6 3 0 7 4 1 8 5
 2 9 6 3 0 7 4 1 8 5
 2 9 6 3 0 7 4 1 8 5
 2 9 6 3 0 7 4 1 8 5
 2 9 6 3 0 7 4 1 8 5
 2 9 6 3 0 7 4 1 8 5
 2 9 6 3 0 7 4 1 8 5
 2 9 6 3 0 7 4 1 8 5
 2 9 6 3 0 7 4 1 8 5
 2 9 6 3 0 7 4 1 8 5

Notice how the digits repeat every 10 digits.

In general, two relatively prime numbers are chosen - often two primes.

In Python (3.x) there is a way to print without a newline by adding the end actual parameter.

Here is the Python code.

print("Hello")
print("World")
print("Hello",end="")
print("World")

Here is the output of the Python code.

Hello
World
HelloWorld

Note: In many cases, text can be constructed via a list and then joined to form the desired text.

If you are testing a program, you may to test it using the sequence every time rather than a different sequence every time.

When you test programs, you would like to have the same output for the same input. If the input/output changes each time run the program, this is harder to do.

Solution: pseudo random number sequences.