A144137 Numbers n such that between n^K and (n+1)^K there are no primes, where K = sqrt(2).

4, 24, 29, 33, 40, 43, 56, 59, 84, 117, 122, 128, 132, 139, 145, 156, 162, 163, 183, 190, 203, 230, 253, 257, 286, 297, 303, 306, 315, 319, 336, 371, 403, 420, 433, 447, 456, 467, 479, 537, 543, 563, 592, 595, 599, 624, 699, 746, 755, 767, 774, 782, 805, 814

Offset: 1

Author

Artur Jasinski, Sep 11 2008

Keywords

• nonn

Examples

			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).
		

Links

• T. D. Noe, Table of n, a(n) for n=1..133 (no other n < 10^6)

Crossrefs

Cf. A014085, A143898, A143935, A144140.

Programs

Mathematica

a = {}; k = Sqrt[2]; Do[If[Length[Select[Range[Ceiling[n^k], Floor[(n + 1)^k]], PrimeQ]] == 0, AppendTo[a, n]], {n, 3000}]; a
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 *)