Hofstadteriana with primes

[Jacques Tramu]

Eric wrote :
>
> Hello SeqFans,
>
> S = 1   3   8   15  26  39  56  75  98  127  158  195  236  279  326...
> d =   2   5   7   11  13  17  19  23  29   31   37   41   43   47 ...
>
> - start S with 1
> - add the smallest prime not yet added and not already present in S
>
> Question:
> - What could be the ratio primes/composites of S?

S :
1       3       8       15      26      39      56      75      98      127 
158     195     236
279     326     379     438     499     566     637     710     789     872 
961     1058    1159
1262    1369    1478    1591    ....

First primes in S  :
3       127     379     499     3137    4759    5701    7853    17681 
24793   25933   28289   30727
68281   70201   76129   86509   109357  114277  143519  146381  170141 
176369  179519  198953  202289 .....


Computed S up to 10000 terms
Number of primes :  551

regards,
JT