[QUOTE=3.14159;227797]If there is a k < b[sup]b[/sup] restriction, b ≥ 1.[/QUOTE]

That was my third suggestion.

[QUOTE=3.14159;227797]If there's no k < b[sup]b[/sup] restriction, b > 1.[/QUOTE]

That would be a fourth way to do it. It has relative density ≈ 0.528 in the primes.

[QUOTE=3.14159;227801]If there is no k < b[sup]b[/sup] restriction, and b = 1 is allowed, it is precisely the same as A000040.

I will begin work on the sequence with the k < b[sup]b[/sup] restriction.[/QUOTE]

sorry CRG I see what he means today lol k*2^1+1 can give all primes.

Also: Is there a command or script that allows printing in numerical order?

[QUOTE=3.14159;227801]If there is no k < b[sup]b[/sup] restriction, and b = 1 is allowed, it is precisely the same as A000040.[/QUOTE]

Neither of my first two sequences restrict k to be less than b^b and both allow b = 1, but neither is A000040. I invite you to re-read #1209.

[QUOTE=3.14159;227804]Also: Is there a command or script that allows printing in numerical order?[/QUOTE]

maybe vecsort could help you in pari but I'm not sure how to use it.

[QUOTE=3.14159;227804]Also: Is there a command or script that allows printing in numerical order?[/QUOTE]

If you put the numbers in a vector, you can use vecsort to order them. vecsort(v) returns a sorted version of v, while vecsort(v,,8) returns a sorted version of v with the duplicates removed.

[QUOTE=science_man_88;227806]maybe vecsort could help you in pari but I'm not sure how to use it.[/QUOTE]

Bingo! sm88 beat me to it.

[QUOTE=CRGreathouse;227808]Bingo! sm88 beat me to it.[/QUOTE]

calls for a celebration I think that's a first lol.

[QUOTE=science_man_88;227803]sorry CRG I see what he means today lol k*2^1+1 can give all primes.[/QUOTE]

You can see that I understand that, since I mention A000040 explicitly in post #1209. But none of my three sequences are equal to A000040, as even a cursory examination will show.

[QUOTE=science_man_88;227809]calls for a celebration I think that's a first lol.[/QUOTE]

I'll lift a glass in your honor. (Literally, why not!)

[QUOTE=CRGreathouse;227810]You can see that I understand that, since I mention A000040 explicitly in post #1209. But none of my three sequences are equal to A000040, as even a cursory examination will show.[/QUOTE]

oh wait k*b^b+1 would give k*1+1 for b=1 still all the primes I think.

doh I fell to his thinking lol.