Ratio (1+b(n+1)) / b(n) for the sequence b = S000304.
2, 6, 12, 6, 198, 24, 210, 1038, 1512, 990, 90, 582, 474, 6630, 7878, 2772, 24972, 25092, 6798, 70074, 11754, 25626, 20010, 4470, 36990, 11928, 69342, 150, 8502, 15504, 14100, 75768, 38502, 7272, 52512, 57552, 74712, 12870, 237768, 48510, 10050, 20832
1
The number a(n) gives approximately the growth ratio for terms in S000304.
T. D. Noe, Plot of 100 terms
T. D. Noe, Table of 100 terms
(Mma) p = 3; Table[k = 1; While[! (PrimeQ[k*p - 1] && PrimeQ[k*p + 1]), k++]; p = k*p - 1; k, {20}]
Cf. S000304.
nonn
T. D. Noe, Oct 20 2014