A111190 Numbers k such that floor(Pi^k - e^k) is prime.

2, 5, 6, 73, 1547, 2714, 4937, 5212, 58775

Offset

1,1

Comments

No more terms through 10000.

If it exists, a(10) > 90000. - J.W.L. (Jan) Eerland, Sep 29 2022

Links

Table of n, a(n) for n=1..9.

Example

floor(Pi^6 - e^6) = 557 is prime, hence 6 is a term.

Mathematica

$MaxExtraPrecision = 10^6; Do[k = Floor[Pi^n - E^n]; If[PrimeQ[k], Print[n]], {n, 1, 10000}]
Select[Range[6000], PrimeQ[Floor[Pi^#-E^#]]&] (* Harvey P. Dale, Jun 02 2014 *)
ParallelTable[If[PrimeQ[Floor[Pi^k-E^k]], k, Nothing], {k, 0, 9*10^4}]//.{}->Nothing (* J.W.L. (Jan) Eerland, Sep 29 2022 *)

Crossrefs

Cf. A181052.

Sequence in context: A288799 A281378 A219117 * A244434 A176007 A009376

Adjacent sequences: A111187 A111188 A111189 * A111191 A111192 A111193

Keyword

nonn,hard,more

Author

Ryan Propper, Oct 23 2005

Extensions

a(9) from J.W.L. (Jan) Eerland, Sep 29 2022

Status

approved