A155931 Squares s(n) such that cube(n)-square(n)-1 and cube(n)+square(n)+1 are primes.

4, 9, 81, 144, 900, 3249, 4356, 7569, 12321, 14400, 38025, 59049, 60516, 77841, 142884, 145161, 186624, 202500, 221841, 230400, 356409, 423801, 576081, 656100, 870489, 974169, 1108809, 1838736, 1855044, 1971216, 1979649, 1988100, 2396304

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

Table of n, a(n) for n=1..33.

Mathematica

lst={}; Do[c=n^3; s=n^2; p1=c-s-1; p2=c+s+1; If[PrimeQ[p1]&&PrimeQ[p2], AppendTo[lst, s]], {n, 7!}]; lst
#^2&/@Select[Range[1600], AllTrue[#^3+{-#^2-1, #^2+1}, PrimeQ]&] (* Harvey P. Dale, Feb 24 2023 *)

Crossrefs

Cf. A155929, A155930

Sequence in context: A359654 A061104 A082381 * A309801 A248245 A368629

Adjacent sequences: A155928 A155929 A155930 * A155932 A155933 A155934

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 30 2009

Status

approved