Prime Number Chains

Now that I have regular Internet access I can resume scrutiny of my numbered days and today's number happens to be 24481 and prime. OEIS A110059 states that 24481 is the member of a sequence such that it is the smallest prime ending a complete Cunningham Chain of the second kind (2x-1) of length n. See my earlier post about Cunningham Chains. The sequence (up to n=13) is:

1. 11
2. 13
3. 5
4. 17041
5. 24481
6. 12338881
7. 1065601
8. 1985902081
9. 219416417281
10. 105230562877441
11. 1422461638625281
12. 444124661486837761
13. 3105111850422067201

Now n=5 for 24481 and so adding 1 and dividing by 2 successively yields 12241, 6121, 3061 and 1531. So the complete chain is:

1531, 3061, 6121, 12241, 24481

The number is also a prime of the form 1+2n+3n^2 (OEIS A122430) and for 24481 the value on n is 90.

This prime number also has the property that it is a number n such that n remains prime through 5 iterations of the function f(x)=3x+10 (OEIS A023338). Applying this function rule yields progressively 73453, 220369, 661117, 1983361 and 5950093 and thus we have the prime number sequence:

24481, 73453, 220369, 661117, 1983361, 5950093

It also turns out that 24481 is a lucky number. To remind myself what that means, I've attached this definition from WolframAlpha:

Write out all odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, .... The first odd number >1 is 3, so strike out every third number from the list: 1, 3, 7, 9, 13, 15, 19, .... The first odd number greater than 3 in the list is 7, so strike out every seventh number: 1, 3, 7, 9, 13, 15, 21, 25, 31, .... 

Numbers remaining after this procedure has been carried out completely are called lucky numbers. The first few are 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, ... (OEIS A000959). Many asymptotic properties of the prime numbers are shared by the lucky numbers. The asymptotic density is 1/lnN, just as the prime number theorem, and the frequency of twin primes and twin lucky numbers are similar. A version of the Goldbach conjecture also seems to hold.

So it would seem that 24481 is indeed an interesting number.