[seqfan] Probability of identical sequences

[Ali Sada]

Hi Everyone, 

If we have two sequences, A and B, with different definitions. However, when we calculate k terms for each sequence, all of these terms are identical. If we can’t prove that definition A equals to definition B, what’s the probability that A and B are identical? Is it zero, since we are dealing with infinite terms? Or is it a function of k?  

This question came to me when I was trying this algorithm: Exchange n and 2n. Each term gets changed only once. 
a(1)=2 and a(2)=1.
a(3)=6 and a(6)=3
etc.
The sequence I got was 
2, 1, 6, 8, 10, 3, 14, 4, 18, 5, 22, 24, 26, 7, 30, 32, 34, 9, 38, 40, 42, 11, 46, 12, 50, 13

This sequence seems identical to A073675 (Rearrangement of natural numbers such that a(n) is the smallest proper divisor of n not included earlier but if no such divisor exists then a(n) is the smallest proper multiple of n not included earlier, subject always to the condition that a(n) is not equal to n.)

This example might not reflect my question above exactly. I am just trying to show why I asked the question.

Best,

Ali