A116581 Primes of the form k^3 - k - 1.

5, 23, 59, 503, 719, 1319, 2729, 3359, 4079, 5813, 9239, 12143, 13799, 24359, 29759, 42839, 46619, 54833, 68879, 91079, 110543, 166319, 195053, 205319, 215939, 262079, 328439, 342929, 357839, 438899, 531359, 635969, 941093, 1124759, 1259603, 1367519, 1442783

Offset: 1

Author

Roger L. Bagula, Mar 22 2006

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Ken Ono and Scott Ahlgren, Weierstrass points on X0(p) and supersingular j-invariants, Mathematische Annalen 325, 2003, pp. 355-368.

Crossrefs

Cf. A002327, A126420, A126421.

Programs

Magma

[ a: n in [1..200] | IsPrime(a) where a is n^3-n-1 ]; // Vincenzo Librandi, Dec 07 2011

Mathematica

Select[Table[n^3-n-1,{n,0,800}],PrimeQ] (* Vincenzo Librandi, Dec 07 2011 *)

Python

from sympy import isprime
def aupton(terms):
  k, alst = 2, []
  while len(alst) < terms:
    if isprime(k**3-k-1): alst.append(k**3-k-1)
    k += 1
  return alst
print(aupton(37)) # Michael S. Branicky, May 23 2021

Formula

a(n) = A126420(A126421(n)). - Elmo R. Oliveira, Apr 20 2025

Extensions

Edited by N. J. A. Sloane, Jan 01 2007

More terms from Artur Jasinski, Jan 01 2007