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 17 results. Next

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

Views

Author

Artur Jasinski, Dec 26 2006

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)

Formula

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

Extensions

Definition corrected by Charles R Greathouse IV, Mar 11 2008

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 *)

A236071 Primes p such that p^4 - p - 1 is prime.

Original entry on oeis.org

2, 5, 7, 11, 13, 23, 53, 61, 71, 79, 137, 139, 193, 229, 239, 251, 293, 317, 373, 433, 523, 599, 601, 683, 727, 859, 877, 887, 911, 991, 1009, 1163, 1229, 1297, 1303, 1429, 1481, 1483, 1789, 1801, 1871, 1999, 2011
Offset: 1

Views

Author

Derek Orr, Jan 19 2014

Keywords

Comments

Primes in A126424.

Examples

			139 is prime and 139^4 - 139 - 1 is prime, so 139 is a member of this sequence.

Links

Crossrefs

Cf. A049408.

Programs

  • Mathematica
    Select[Prime[Range[400]],PrimeQ[#^4-#-1]&] (* Harvey P. Dale, Jan 20 2019 *)
  • PARI
    s=[]; forprime(p=2, 3000, if(isprime(p^4-p-1), s=concat(s, p))); s \\ Colin Barker, Jan 19 2014
  • Python
    import sympy
from sympy import isprime
{print(p) for p in range(10**4) if isprime(p**4-p-1) and isprime(p)}

A236759 Numbers n such that n^4+n-1 is prime.

Original entry on oeis.org

2, 3, 6, 9, 10, 12, 13, 16, 17, 20, 23, 26, 28, 31, 33, 40, 43, 44, 54, 58, 72, 77, 92, 93, 98, 105, 110, 117, 119, 120, 122, 125, 132, 143, 157, 164, 182, 201, 204, 205, 229, 231, 266, 275, 279, 286, 288, 290, 292, 293, 304, 309, 318
Offset: 1

Views

Author

Derek Orr, Jan 30 2014

Keywords

Examples

			98^4 + 98 - 1 = 92236913 is prime. Thus, 98 is a member of this sequence.

Crossrefs

Cf. A049408, A126424.

Programs

  • Mathematica
    Select[Range[400],PrimeQ[#^4+#-1]&] (* Harvey P. Dale, Jul 15 2020 *)
  • PARI
    s=[]; for(n=1, 400, if(isprime(n^4+n-1), s=concat(s, n))); s \\ Colin Barker, Jan 31 2014
  • Python
    import sympy
from sympy import isprime
{print(n) for n in range(10**3) if isprime(n**4+n-1)}

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 *)

A236761 Numbers n such that n^4-n+1 is prime.

Original entry on oeis.org

3, 6, 9, 13, 16, 18, 19, 24, 33, 39, 43, 45, 46, 60, 63, 64, 69, 75, 78, 79, 85, 91, 94, 105, 106, 108, 109, 115, 121, 129, 138, 174, 175, 183, 195, 198, 205, 210, 220, 249, 250, 276, 289, 295, 300, 309, 313, 318, 324, 343, 346, 348
Offset: 1

Views

Author

Derek Orr, Jan 30 2014

Keywords

Examples

			115^4 - 115 + 1 = 174900511 is prime. Thus, 115 is a member of this sequence.

Crossrefs

Cf. A049408, A126424.

Programs

  • Mathematica
    Select[Range[400],PrimeQ[#^4-#+1]&] (* Harvey P. Dale, Jun 03 2015 *)
  • PARI
    s=[]; for(n=1, 400, if(isprime(n^4-n+1), s=concat(s, n))); s \\ Colin Barker, Jan 31 2014
  • Python
    import sympy
from sympy import isprime
{print(n) for n in range(10**3) if isprime(n**4-n+1)}
Showing 1-10 of 17 results. Next

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

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