Least lower twin prime of the form 2*n*k ± 1.
3, 3, 5, 71, 29, 11, 41, 191, 17, 59, 197, 71, 311, 419, 29, 191, 101, 71, 227, 239, 41, 659, 137, 191, 149, 311, 107, 2687, 347, 59, 1301, 191, 197, 1019, 419, 71, 1997, 227, 311, 239, 1229, 419, 1031, 1319, 179, 827, 281, 191, 881, 599, 101, 311, 6359, 107, 659
1
The first number of every twin-prime pair eventually appears.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Eric W. Weisstein, MathWorld: Twin Primes
Example: the fourth term is 71 because the twin-prime pair (71,73) is the first pair of the form 8*k ± 1.
(Mma) mx = 10^5; Flatten[Table[Select[2*n*Range[mx] - 1, PrimeQ[#] && PrimeQ[#+2] &, 1], {n, mx/100}]]
Cf. A001097 (twin primes).
nonn
T. D. Noe, May 21 2015