cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

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

Original entry on oeis.org

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

Views

Author

Artur Jasinski, Dec 26 2006

Keywords

Links

Crossrefs

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

Programs

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

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

Views

Author

Artur Jasinski, Dec 26 2006

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [n^4-n-1: n in [1..40]]; // Vincenzo Librandi, Aug 30 2011
  • Mathematica
    a = {}; Do[AppendTo[a, x^4 - x - 1], {x, 1, 100}]; a

Formula

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

Views

Author

Artur Jasinski, Dec 26 2006

Keywords

Comments

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

Links

Crossrefs

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

Programs

Formula

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

Views

Author

Artur Jasinski, Dec 26 2006

Keywords

Comments

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

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)

Formula

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

Views

Author

Artur Jasinski, Dec 26 2006

Keywords

Links

Crossrefs

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

Programs

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

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

Views

Author

Artur Jasinski, Dec 26 2006

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)

A126435 Primes of the form n^7-n-1.

Original entry on oeis.org

2097143, 1801088519, 21869999969, 42618442943, 78364164059, 137231006639, 194754273839, 435817657169, 678223072799, 1174711139783, 1727094849479, 3938980639103, 4398046511039, 4902227890559, 6722988818363, 19203908986079
Offset: 1

Views

Author

Artur Jasinski, Dec 26 2006

Keywords

Comments

All terms end in 3 or 9. - Robert Israel, Jul 22 2019

Links

Crossrefs

Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423, A126424, A126425, A126426, A126427, A126427, A126428, A126429, A126430, A126431, A126432 A126433, A126434.

Programs

  • Maple
    map(t -> t^7-t-1, select(t -> isprime(t^7-t-1), [$1..10^4])); # Robert Israel, Jul 22 2019
  • Mathematica
    k = 7; a = {}; Do[If[PrimeQ[x^k - x - 1], AppendTo[a, x^k - x - 1]], {x, 1, 100}]; a
Select[Table[n^7-n-1,{n,80}],PrimeQ] (* Harvey P. Dale, Jun 20 2020 *)

A126437 Primes of the form k^8-k-1.

Original entry on oeis.org

1679609, 5764793, 99999989, 4294967279, 282429536453, 377801998307, 5352009260441, 16815125390579, 39062499999949, 72301961339081, 83733937890569, 281474976710591, 513798374428571, 1113034787454899
Offset: 1

Views

Author

Artur Jasinski, Dec 26 2006

Keywords

Links

Crossrefs

Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423, A126424, A126425, A126426, A126427, A126427, A126428, A126429, A126430, A126431, A126432 A126433, A126434, A126434.

Programs

  • Mathematica
    k = 8; a = {}; Do[If[PrimeQ[x^k - x - 1], AppendTo[a, x^k - x - 1]], {x, 1, 100}]; a
Select[Table[k^8-k-1,{k,80}],PrimeQ] (* Harvey P. Dale, Nov 06 2021 *)

A126438 Primes of the form n^9-n-1.

Original entry on oeis.org

509, 262139, 10077689, 387420479, 68719476719, 118587876479, 1207269217769, 7625597484959, 10578455953379, 129961739795039, 327381934393919, 1628413597910399, 1953124999999949, 5416169448144839, 10077695999999939
Offset: 1

Views

Author

Artur Jasinski, Dec 26 2006

Keywords

Links

Crossrefs

Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423, A126424, A126425, A126426, A126427, A126427, A126428, A126429, A126430, A126431, A126432 A126433, A126434, A126435, A126436, A126437.

Programs

  • Mathematica
    k = 9; a = {}; Do[If[PrimeQ[x^k - x - 1], AppendTo[a, x^k - x - 1]], {x, 1, 100}]; a
Select[Table[n^9-n-1,{n,100}],PrimeQ] (* Harvey P. Dale, Mar 09 2016 *)

A126439 Least prime of the form x^n-x-1.

Original entry on oeis.org

5, 5, 13, 29, 61, 2097143, 1679609, 509, 1021, 8589934583, 4093, 67108859, 16381, 470184984569, 4294967291, 2218611106740436979, 68719476731, 1350851717672992079, 1048573, 10460353199, 4194301, 20013311644049280264138724244295359, 16777213, 108347059433883722041830239, 20282409603651670423947251285999, 58149737003040059690390159, 72057594037927931, 536870909, 999999999999999999999999999989
Offset: 2

Views

Author

Artur Jasinski, Dec 26 2006, Jan 19 2007

Keywords

Crossrefs

Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423, A126424, A126425, A126426, A126427, A126427, A126428, A126429, A126430, A126431, A126432 A126433, A126434, A126435, A126436, A126437, A126438.

Programs

  • Mathematica
    a = {}; Do[k = 2; While[ ! PrimeQ[k^n -k - 1], k++ ]; AppendTo[a, k^n - k - 1], {n, 2, 30}]; a (*Artur Jasinski*)
Showing 1-10 of 10 results.

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