A155930 Cubes c(n) such that cube(n)-square(n)-1 and cube(n)+square(n)+1 are primes.

8, 27, 729, 1728, 27000, 185193, 287496, 658503, 1367631, 1728000, 7414875, 14348907, 14886936, 21717639, 54010152, 55306341, 80621568, 91125000, 104487111, 110592000, 212776173, 275894451, 437245479, 531441000, 812166237

Offset

1,1

Comments

2^3-2^2-1=3;2^3+2^2+1=13, 3^3-3^2-1=17;3^3+3^2+1=37, ...

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

lst={}; Do[c=n^3; s=n^2; p1=c-s-1; p2=c+s+1; If[PrimeQ[p1]&&PrimeQ[p2], AppendTo[lst, c]], {n, 7!}]; lst
cspQ[n_]:=Module[{x3=n^3, x2=n^2}, And@@PrimeQ[{x3-x2-1, x3+x2+1}]]; Select[ Range[ 1000], cspQ]^3 (* Harvey P. Dale, Jun 12 2014 *)

Crossrefs

Cf. A155929

Sequence in context: A348585 A007235 A029789 * A100519 A272245 A115701

Adjacent sequences: A155927 A155928 A155929 * A155931 A155932 A155933

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 30 2009

Status

approved