A137475 Positive numbers k such that k^3 - (k+1)^2 and k^3 + (k+1)^2 are both primes.

3, 8, 15, 35, 39, 45, 50, 65, 92, 99, 122, 140, 164, 167, 170, 198, 237, 284, 287, 297, 339, 354, 408, 435, 515, 522, 552, 582, 594, 650, 668, 708, 725, 737, 753, 830, 1010, 1068, 1098, 1128, 1253, 1295, 1373, 1424, 1502, 1548, 1553, 1599, 1704, 1779, 1817

Offset

1,1

Links

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

Example

3^3 +- 4^2 -> (11, 43) (both primes);
167^3 +- 168^2 = 4657463 +- 28224 -> (4629239, 4685687) (both primes).

Mathematica

Select[Range[900], PrimeQ[ #^3-(#+1)^2]&&PrimeQ[ #^3+(#+1)^2]&]
bpQ[n_]:=Module[{a=(n+1)^2}, AllTrue[n^3+{a, -a}, PrimeQ]]; Select[Range[ 2, 2000], bpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 17 2019 *)

Prog

(Magma) [n: n in [2..500] | IsPrime(n^3-(n+1)^2)and IsPrime(n^3 +(n+1)^2)] // Vincenzo Librandi, Nov 24 2010

Crossrefs

Sequence in context: A255835 A032234 A032255 * A176433 A132810 A032159

Adjacent sequences: A137472 A137473 A137474 * A137476 A137477 A137478

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2008

Extensions

More terms from Vincenzo Librandi, Mar 26 2010

Status

approved