A137461 Positive numbers k such that k^3 + k - 1 and k^3 - k + 1 are both primes.

4, 7, 10, 15, 21, 25, 39, 52, 87, 120, 129, 139, 189, 202, 259, 286, 316, 376, 391, 466, 472, 486, 510, 532, 574, 631, 642, 684, 685, 739, 750, 769, 882, 972, 987, 991, 1029, 1074, 1092, 1201, 1212, 1231, 1320, 1326, 1456, 1506, 1522, 1524, 1539, 1575, 1632

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

7^3 +- 6 -> (337, 349) (both prime);
139^3 +- 138 -> (2685481, 2685757) (both prime).

Maple

filter:= k -> isprime(k^3+k-1) and isprime(k^3-k+1):
select(filter, [$1..10000]); # Robert Israel, Jun 19 2025

Mathematica

Select[Range[999], PrimeQ[ #^3-(#-1)]&&PrimeQ[ #^3+(#-1)]&]

Prog

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

Crossrefs

Sequence in context: A310706 A095875 A071408 * A137379 A342761 A096676

Adjacent sequences: A137458 A137459 A137460 * A137462 A137463 A137464

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2008

Extensions

More terms from Vincenzo Librandi, Mar 26 2010

Status

approved