A126421 -id:A126421 - cp's OEIS frontend

A126424 Numbers k for which k^4-k-1 is prime.

2, 4, 5, 6, 7, 9, 11, 13, 16, 20, 23, 26, 39, 40, 42, 44, 50, 53, 55, 57, 60, 61, 68, 71, 77, 79, 82, 92, 110, 111, 112, 123, 137, 139, 140, 147, 153, 154, 156, 169, 172, 174, 177, 183, 187, 189, 193, 198, 207, 214, 229, 230, 231, 239, 251, 258, 259, 272, 274, 279

Offset: 1

Artur Jasinski, Dec 26 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423.

a = {}; Do[If[PrimeQ[x^4 - x - 1], AppendTo[a, x]], {x, 1, 1000}]; a

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

Original entry on oeis.org

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

Roger L. Bagula, Mar 22 2006

nonn

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.

Cf. A002327, A126420, A126421.

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

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

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

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

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

More terms from Artur Jasinski, Jan 01 2007

A126422 Primes of the form k^4-k-1.

Original entry on oeis.org

13, 251, 619, 1289, 2393, 6551, 14629, 28547, 65519, 159979, 279817, 456949, 2313401, 2559959, 3111653, 3748051, 6249949, 7890427, 9150569, 10555943, 12959939, 13845779, 21381307, 25411609, 35152963, 38950001, 45212093

Offset: 1

Artur Jasinski, Dec 26 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A002327, A002328, A116581, A126420, A126421, A126423, A126424.

a = {}; Do[If[PrimeQ[x^4 - x - 1], AppendTo[a, x^4 - x - 1]], {x, 1, 100}]; a
Select[Table[n^4-n-1,{n,100}],PrimeQ] (* Harvey P. Dale, Aug 27 2013 *)

a(n) = A126423(A126424(n)). - Amiram Eldar, Mar 13 2020

Definition corrected by Charles R Greathouse IV, Mar 11 2008

A126423 a(n) = n^4 - n - 1.

Original entry on oeis.org

-1, 13, 77, 251, 619, 1289, 2393, 4087, 6551, 9989, 14629, 20723, 28547, 38401, 50609, 65519, 83503, 104957, 130301, 159979, 194459, 234233, 279817, 331751, 390599, 456949, 531413, 614627, 707251, 809969, 923489, 1048543, 1185887, 1336301, 1500589, 1679579, 1874123, 2085097, 2313401, 2559959

Offset: 1

Artur Jasinski, Dec 26 2006

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A002327, A002328, A116581, A126420, A126421, A126422.

[n^4-n-1: n in [1..40]]; // Vincenzo Librandi, Aug 30 2011

a = {}; Do[AppendTo[a, x^4 - x - 1], {x, 1, 100}]; a

From Elmo R. Oliveira, Aug 29 2025: (Start)
G.f.: x*(-1 + 18*x + 2*x^2 + 6*x^3 - x^4)/(1-x)^5.
E.g.f.: 1 + (-1 + 7*x^2 + 6*x^3 + x^4)*exp(x).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 5. (End)

A126426 a(n) = n^5 - n - 1.

Original entry on oeis.org

-1, 29, 239, 1019, 3119, 7769, 16799, 32759, 59039, 99989, 161039, 248819, 371279, 537809, 759359, 1048559, 1419839, 1889549, 2476079, 3199979, 4084079, 5153609, 6436319, 7962599, 9765599, 11881349, 14348879, 17210339, 20511119, 24299969, 28629119, 33554399, 39135359, 45435389

Offset: 1

Artur Jasinski, Dec 26 2006

Every number gives remainder 29 when divided by 30, remainder 9 when divided by 10, and remainder 4 when divided by 5.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423, A126424, A126425.

[n^5-n-1: n in [1..40]]; // Vincenzo Librandi, Aug 30 2011

A126426:=n->n^5-n-1: seq(A126426(n), n=1..50); # Wesley Ivan Hurt, Jan 17 2017

a = {}; Do[AppendTo[a, x^5 - x - 1], {x, 1, 100}]; a
Table[n^5-n-1,{n,40}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{-1,29,239,1019,3119,7769},40] (* Harvey P. Dale, Jul 02 2018 *)

a(n)=n^5-n-1 \\ Charles R Greathouse IV, Oct 07 2015

G.f.: x*(x^5-5*x^4+40*x^3+50*x^2+35*x-1)/(1-x)^6. - Colin Barker, Oct 07 2012

A126425 Primes of the form k^5-k-1.

Original entry on oeis.org

29, 239, 1019, 3119, 99989, 161039, 759359, 1048559, 1419839, 2476079, 3199979, 4084079, 14348879, 17210339, 24299969, 45435389, 60466139, 164916179, 254803919, 312499949, 550731719, 1934917559, 2373046799, 3707398349

Offset: 1

Artur Jasinski, Dec 26 2006

nonn

Every number give rest 29 when divided 30, rest 9 when divided 10, rest 4 when divided 5

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423, A126424, A126426, A126427.

a = {}; Do[If[PrimeQ[x^5 - x - 1], AppendTo[a, x^5 - x - 1]], {x, 1, 100}]; a
Select[Table[k^5-k-1,{k,90}],PrimeQ] (* Harvey P. Dale, Apr 21 2024 *)

a(n) = A126426(A126427(n)). - Amiram Eldar, Mar 13 2020

A126427 Numbers k for which k^5-k-1 is prime.

Original entry on oeis.org

2, 3, 4, 5, 10, 11, 15, 16, 17, 19, 20, 21, 27, 28, 30, 34, 36, 44, 48, 50, 56, 72, 75, 82, 84, 97, 101, 103, 105, 109, 113, 117, 130, 133, 141, 154, 157, 163, 177, 179, 188, 197, 204, 207, 218, 240, 248, 249, 250, 252, 262, 268, 281, 283, 285, 286, 291, 301, 305, 315

Offset: 1

Artur Jasinski, Dec 26 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423, A126424, A126425, A126426.

a = {}; Do[If[PrimeQ[x^5 - x - 1], AppendTo[a, x]], {x, 1, 1000}]; a

A236477 Numbers k such that k^3 - k + 1 is prime.

Original entry on oeis.org

2, 4, 6, 7, 10, 11, 14, 15, 19, 21, 22, 25, 26, 31, 35, 39, 41, 42, 45, 50, 52, 54, 57, 62, 75, 77, 84, 85, 87, 90, 92, 95, 99, 101, 102, 106, 111, 116, 120, 125, 129, 130, 132, 134, 136, 139, 140, 141, 147, 155, 167, 169, 176, 189, 195, 202, 221, 230, 237

Offset: 1

Derek Orr, Jan 26 2014

nonn

			26^3 - 26 + 1 = 17551 is prime. So 26 is a member of this sequence.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A049407, A126421, A236478.

Select[Range[250],PrimeQ[#^3-#+1]&] (* Harvey P. Dale, Dec 06 2017 *)

s=[]; for(n=1, 500, if(isprime(n^3-n+1), s=concat(s, n))); s \\ Colin Barker, Jan 27 2014

import sympy
from sympy import isprime
{print(n) for n in range(10**3) if isprime(n**3-n+1)}

More terms from Colin Barker, Jan 27 2014

A126434 Primes of the form k^6-k-1.

Original entry on oeis.org

61, 4091, 15619, 46649, 2985971, 16777199, 24137551, 63999979, 4750104199, 8303765579, 27680640569, 30840979399, 34296447191, 68719476671, 117648999929, 351298031531, 377149515539, 606355001251, 689869780961

Offset: 1

Artur Jasinski, Dec 26 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423, A126424, A126425, A126426, A126427.

k = 6; a = {}; Do[If[PrimeQ[x^k - x - 1], AppendTo[a, x^k - x - 1]], {x, 1, 100}]; a
Select[Table[n^6-n-1,{n,200}],PrimeQ] (* Harvey P. Dale, Mar 28 2013 *)

A236475 Numbers k such that k^3 + k - 1 is prime.

Original entry on oeis.org

3, 4, 7, 10, 15, 16, 18, 21, 25, 27, 33, 36, 39, 43, 46, 51, 52, 55, 63, 73, 78, 81, 87, 93, 94, 96, 100, 103, 105, 109, 112, 115, 117, 120, 124, 127, 129, 135, 139, 145, 150, 151, 165, 166, 171, 178, 189, 192, 198, 199

Offset: 1

Derek Orr, Jan 26 2014

nonn

			46^3 + 46 - 1 = 97381 is prime. So 46 is a member of this sequence.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A049407, A126421.

Select[Range[200],PrimeQ[#^3+#-1]&] (* Harvey P. Dale, Sep 02 2022 *)

s=[]; for(n=1, 500, if(isprime(n^3+n-1), s=concat(s, n))); s \\ Colin Barker, Jan 27 2014

import sympy
from sympy import isprime
{print(n) for n in range(10**3) if isprime(n**3+n-1)}

cp's OEIS Frontend

A126424 Numbers k for which k^4-k-1 is prime.

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

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A126422 Primes of the form k^4-k-1.

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A126423 a(n) = n^4 - n - 1.

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A126426 a(n) = n^5 - n - 1.

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A126425 Primes of the form k^5-k-1.

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A126427 Numbers k for which k^5-k-1 is prime.

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A236477 Numbers k such that k^3 - k + 1 is prime.

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