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.

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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 *)

A088502 Numbers n such that (n^2 - 5)/4 is prime.

Original entry on oeis.org

5, 7, 9, 11, 13, 17, 19, 21, 23, 27, 31, 33, 39, 41, 43, 49, 53, 57, 61, 63, 71, 77, 79, 83, 89, 91, 93, 97, 101, 107, 109, 111, 113, 119, 121, 129, 131, 133, 137, 141, 153, 167, 171, 173, 179, 187, 189, 193, 201, 203, 207, 229, 231, 241, 251, 253, 261, 263, 269
Offset: 1

Views

Author

Pierre CAMI, Nov 13 2003

Keywords

Comments

Under Bunyakovsky's conjecture this sequence is infinite. - Charles R Greathouse IV, Dec 28 2011

Examples

			(23*23 - 5)/4 = 131, 131 is prime, 23 is the 9th n of the sequence.

Links

Crossrefs

Cf. A002327, A002328, A110013.

Programs

Formula

a(n) = 2*A002328(n) - 1 = Sqrt(A110013(n)). - Ray Chandler, Sep 07 2005

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 *)

A131530 Numbers k such that k^2 - k - 1 and k^2 - k + 1 are twin primes.

Original entry on oeis.org

3, 4, 6, 7, 9, 16, 21, 22, 25, 39, 42, 51, 55, 60, 67, 90, 102, 132, 139, 142, 154, 156, 165, 177, 189, 204, 207, 210, 216, 219, 232, 237, 247, 289, 291, 310, 315, 352, 379, 396, 406, 454, 456, 457, 496, 501, 519, 531, 552, 561, 625, 645, 669, 687, 721, 729, 744
Offset: 1

Views

Author

Pierre CAMI, Aug 26 2007

Keywords

Links

Crossrefs

Intersection of A002328 and A055494. - Michel Marcus, Jan 24 2018

Programs

  • Magma
    [n: n in [0..500] | IsPrime(n^2-n-1) and IsPrime(n^2-n+1)]; // Vincenzo Librandi, Nov 23 2010
  • Mathematica
    Select[Range[744],AllTrue[{#^2-#-1,#^2-#+1},PrimeQ]&] (* James C. McMahon, Feb 25 2025 *)

A173179 Numbers n such that n^4-n^3-n^2-n-1 is prime.

Original entry on oeis.org

3, 8, 9, 11, 14, 17, 18, 20, 24, 27, 38, 41, 45, 48, 50, 51, 56, 59, 60, 62, 63, 71, 77, 78, 81, 84, 86, 87, 90, 92, 93, 95, 101, 111, 113, 114, 119, 146, 147, 153, 155, 171, 179, 186, 204, 207, 219, 225, 230, 231, 233, 234, 240, 246, 254, 255, 267, 284, 287, 291
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 11 2010

Keywords

Comments

All terms == 0 or 2 (mod 3). - Robert Israel, Mar 09 2020

Links

Crossrefs

Cf. A125082, A002328, A162294.

Programs

  • Magma
    [n: n in [2..350] | IsPrime(n^4 - n^3 - n^2 - n - 1)]; // Vincenzo Librandi, Mar 16 2020
  • Maple
    select(t -> isprime(t^4-t^3-t^2-t-1), [$2..1000]); # Robert Israel, Mar 09 2020
  • Mathematica
    f[n_]:=n^4-n^3-n^2-n-1;Select[Range[6! ],PrimeQ[f[ #1]]&]
  • PARI
    is(n)=isprime(n^4-n^3-n^2-n-1) \\ Charles R Greathouse IV, Jun 06 2017

Extensions

Edited by N. J. A. Sloane, Apr 10 2010

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 *)

A236056 Numbers k such that k^2 +- k +- 1 is prime for all four possibilities.

Original entry on oeis.org

3, 6, 21, 456, 1365, 2205, 2451, 2730, 8541, 18486, 32199, 32319, 32781, 45864, 61215, 72555, 72561, 82146, 83259, 86604, 91371, 95199, 125334, 149331, 176889, 182910, 185535, 210846, 225666, 226254, 288420, 343161, 350091, 403941, 411501, 510399, 567204
Offset: 1

Views

Author

Derek Orr, Jan 18 2014

Keywords

Comments

The only prime in this sequence is a(1) = 3.

Examples

			1365^2 + 1365 + 1 = 1864591,
1365^2 + 1365 - 1 = 1864589,
1365^2 - 1365 + 1 = 1861861, and
1365^2 - 1365 - 1 = 1861859 are all prime, so 1365 is a term of this sequence.

Crossrefs

Numbers in the intersection of A002384, A045546, A055494, and A002328.
Numbers in the intersection of A131530 and A088485.

Programs

  • Maple
    q:= k-> andmap(isprime, [seq(seq(k^2+i+j, j=[k, -k]), i=[1, -1])]):
select(q, [3*t$t=1..200000])[];  # Alois P. Heinz, Feb 25 2020
  • Mathematica
    Select[Range[568000],AllTrue[Flatten[{#^2+#+{1,-1},#^2-#+{1,-1}},1],PrimeQ]&] (* Harvey P. Dale, Jul 31 2022 *)
  • Python
    import sympy
from sympy import isprime
{print(p) for p in range(10**6) if isprime(p**2+p+1) and isprime(p**2-p+1) and isprime(p**2+p-1) and isprime(p**2-p-1)}

A236171 Numbers k such that k^2 - k - 1, k^3 - k - 1, and k^4 - k - 1 are all prime.

Original entry on oeis.org

4, 9, 11, 16, 55, 60, 71, 189, 361, 450, 469, 669, 1261, 1351, 1490, 1591, 2101, 2254, 2396, 2594, 3774, 3866, 4011, 5375, 5551, 5840, 6070, 7336, 7545, 7666, 7735, 8105, 8255, 9825, 10525, 11621, 12100, 13084, 13454
Offset: 1

Views

Author

Derek Orr, Jan 19 2014

Keywords

Examples

			3866^2 - 3866 - 1, 3866^3 - 3866 - 1, and 3866^4 - 3866 - 1 are all prime, so 3866 is a member of this sequence.

Links

Crossrefs

Cf. A002328, A126421, A126424.

Programs

  • Mathematica
    Select[Range[15000], And @@ PrimeQ[#^Range[2, 4] - # - 1] &] (* Amiram Eldar, Mar 21 2020 *)
  • PARI
    s=[]; for(n=1, 20000, if(isprime(n^2-n-1) && isprime(n^3-n-1) && isprime(n^4-n-1), s=concat(s, n))); s \\ Colin Barker, Jan 20 2014
  • Python
    import sympy
from sympy import isprime
{print(n) for n in range(10**5) if isprime(n**2-n-1) and isprime(n**3-n-1) and isprime(n**4-n-1)}

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*)
Previous Showing 11-20 of 28 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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