A137473 Positive numbers k such that k^3 +- (k-1)^2 are primes.

3, 6, 7, 13, 21, 73, 75, 90, 91, 97, 106, 115, 157, 201, 208, 238, 291, 300, 315, 358, 385, 405, 420, 460, 505, 523, 540, 651, 658, 798, 810, 825, 927, 942, 1000, 1105, 1125, 1135, 1186, 1197, 1278, 1315, 1365, 1378, 1380, 1410, 1417, 1476, 1480, 1483, 1557

Offset

1,1

Links

Table of n, a(n) for n=1..51.

Example

3^3 +- 2^2 -> (23, 31) (both primes);
7^3 +- 6^2 -> (307, 379) (both primes).

Mathematica

Select[Range[900], PrimeQ[ #^3-(#-1)^2]&&PrimeQ[ #^3+(#-1)^2]&]

Prog

(Magma) [n: n in [0..500] | IsPrime(n^3-(n-1)^2)and IsPrime(n^3 +(n-1)^2)] // Vincenzo Librandi, Nov 24 2010

Crossrefs

Sequence in context: A124132 A064291 A245394 * A303604 A349680 A255683

Adjacent sequences: A137470 A137471 A137472 * A137474 A137475 A137476

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2008

Extensions

More terms from Vincenzo Librandi, Mar 26 2010

Status

approved