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%I #16 Jul 31 2021 16:18:16
%S 4,24,29,33,40,43,56,59,84,117,122,128,132,139,145,156,162,163,183,
%T 190,203,230,253,257,286,297,303,306,315,319,336,371,403,420,433,447,
%U 456,467,479,537,543,563,592,595,599,624,699,746,755,767,774,782,805,814
%N Numbers n such that between n^K and (n+1)^K there are no primes, where K = sqrt(2).
%H T. D. Noe, <a href="/A144137/b144137.txt">Table of n, a(n) for n=1..133</a> (no other n < 10^6)
%e a(1)=4 because in range 4^sqrt(2) = 7.10299... and (4+1)^sqrt(2) = 9.73852... there are no primes (8 and 9 aren't primes).
%t a = {}; k = Sqrt[2]; Do[If[Length[Select[Range[Ceiling[n^k], Floor[(n + 1)^k]], PrimeQ]] == 0, AppendTo[a, n]], {n, 3000}]; a
%t Select[Range[850],PrimePi[(#+1)^Sqrt[2]]-PrimePi[#^Sqrt[2]]==0&] (* or *) SequencePosition[PrimePi[Range[850]^Sqrt[2]],{x_,x_}][[All,1]] (* _Harvey P. Dale_, Jul 31 2021 *)
%Y Cf. A014085, A143898, A143935, A144140.
%K nonn
%O 1,1
%A _Artur Jasinski_, Sep 11 2008