Smallest number k > 0 such that the interval (k^2,(k+1)^2) contains n pairs of twin primes.
1, 2, 10, 28, 45, 57, 150, 117, 196, 295, 264, 312, 466, 386, 568, 634, 689, 655, 779, 771, 724, 907, 1036, 1109, 1162, 1044, 1304, 1303, 1354, 1492, 1753, 1844, 2005, 1757, 2370, 1986, 2281, 2549, 2334, 2213, 2789, 3090, 2758, 2989, 3072, 3013, 2900, 3715, 3516
0
T. D. Noe, Plot of 501 terms
T. D. Noe, Table of 501 terms
(Mma) s = Table[Select[Range[n^2 + 1, (n + 1)^2 - 1], PrimeQ[# - 1] && PrimeQ[# + 1] &], {n, 20000}]; Join[{1}, Floor[Sqrt[Table[Select[s, Length[#] == n &][[1, 1]], {n, 100}]]]]
Cf. A099154 (conjecturally, the largest k such that [k^2,(k+1)^2] contains n pairs of twin primes).
nonn
T. D. Noe, Oct 07 2014