Number of pairs twin primes between f^n and f^(n+1) (where f = e^2 = (2.718281828…)^2).
2, 4, 15, 60, 291, 1454, 7786, 43646, 250392, 1487719
0
The two pairs of twin primes between 1 and e^2 are (3,5) and {5,7}.
T. D. Noe, Plot of 10 terms
(Mma) f = E^2; Table[s = Select[Range[Ceiling[f^n], Floor[f^(n + 1)]], PrimeQ]; Length[Intersection[s, s + 2]], {n, 0, 9}]
Cf. A061273 (primes between powers of e), S000187.
nonn
T. D. Noe, Aug 11 2014