Simili-primes

[hv at crypt.org]

"Eric Angelini" <Eric.Angelini at kntv.be> wrote:
:
:http://www.cetteadressecomportecinquantesignes.com/RuleCK.htm

The general rule for sequence <k> is: define 2 as the first k-prime
number, then repeatedly take the k'th following number not divisible
by an existing k-prime as the next k-prime number.

If you remove the initial condition, so that the first entry becomes
k+1, you get another family of sequences:

k=1: primes
k=2: 3 5 8 13 17 22 28 31 38 43 47 53 59 67 73 77 82 89 97 101 107 113 121 127
k=3: 4 7 11 17 23 27 31 39 45 53 59 67 74 82 87 95 103 111 122 127 131 141 146
k=4: 5 9 14 21 26 33 39 46 51 59 67 73 79 87 93 101 109 116 123 129 137 143 152
[...]
k=10: 11 21 32 45 56 69 80 93 106 118 131 145 157 170 182 196 208 222 235 248

It would be interesting to investigate the density of these two families -
we could end up with yet more classes of zeta functions to plague us. :)

Hugo