Lucky Numbers

I haven't devoted a entire post to lucky numbers before, even though I have mentioned them (Prime Number Chains). They occur with about the same frequency as prime numbers but whereas WolframAlpha makes a note of prime numbers, it does not mention lucky numbers. So far they just pass by unnoticed. For the sake of completeness, let's define a lucky number once again (taken 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.

The OEIS site also has a list of lucky numbers between 1 and 200000. I've extracted a list of those that are coming up for me:

2495th lucky number: 24727

2496th lucky number: 24729

2497th lucky number: 24733 lucky and prime

2498th lucky number: 24739

2499th lucky number: 24741

2500th lucky number: 24759

2501st lucky number: 24763 lucky and prime

2502nd lucky number: 24771

2503rd lucky number: 24783

2504th lucky number: 24789

2505th lucky number: 24805

2506th lucky number: 24811

2507th lucky number: 24829

2508th lucky number: 24831

2509th lucky number: 24843

2510th lucky number: 24855

2511th lucky number: 24865

2512th lucky number: 24873

2513th lucky number: 24877 lucky and prime

2514th lucky number: 24895

2515th lucky number: 24907 lucky and prime

2516th lucky number: 24909

2517th lucky number: 24933

2518th lucky number: 24951

2519th lucky number: 24957

2520th lucky number: 24963

2521st lucky number: 24985

2522nd lucky number: 24991

I'll begin entering these into my calendar so that I'm reminded on what numbers are lucky as they occur.