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.

Previous Showing 11-17 of 17 results.

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 *)

A236072 Numbers n such that n^4 + n + 1 and n^4 - n - 1 are prime.

Original entry on oeis.org

2, 5, 6, 9, 11, 26, 44, 60, 77, 147, 239, 384, 545, 690, 770, 779, 1071, 1127, 1190, 1271, 1296, 1331, 1506, 1659, 1707, 1871, 1880, 1986, 2037, 2442, 2520, 2541, 2714, 2960, 2982, 3045, 3060, 3110, 3189, 3287, 3464, 3609
Offset: 1

Views

Author

Derek Orr, Jan 19 2014

Keywords

Examples

			384^4 + 384 + 1 and 384^4 - 384 - 1 are both prime, so 384 is a member of this sequence.

Links

Crossrefs

Numbers in both A126424 and A049408.

Programs

  • Mathematica
    Select[Range[4000],AllTrue[#^4+{#+1,-#-1},PrimeQ]&] (* Harvey P. Dale, Jan 20 2025 *)
  • PARI
    s=[]; for(n=1, 4000, if(isprime(n^4+n+1) && isprime(n^4-n-1), s=concat(s, n))); 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**4+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)}

A236763 Numbers n such that n^4 - n +/- 1 are twin primes.

Original entry on oeis.org

6, 9, 13, 16, 39, 60, 79, 174, 183, 198, 295, 361, 393, 481, 540, 669, 705, 715, 765, 781, 889, 975, 1078, 1149, 1218, 1260, 1288, 1294, 1351, 1363, 1503, 1600, 1611, 1701, 1713, 1911, 2041, 2254, 2298, 2484, 2553, 2625, 2899, 2946, 2959
Offset: 1

Views

Author

Derek Orr, Jan 30 2014

Keywords

Examples

			975^4-975+1 (903687889651) and 975^4-975-1 (903687889649) are twin primes. Thus, 975 is a member of this sequence.

Links

Crossrefs

Intersection of A236761 and A126424.

Programs

  • Mathematica
    Select[Range[3000],AllTrue[#^4-#+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 27 2014 *)
  • PARI
    s=[]; for(n=1, 3000, if(isprime(n^4-n+1)&&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**4) if isprime(n**4-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*)

A177091 Numbers n such that n^4-n-1 is not prime.

Original entry on oeis.org

3, 8, 10, 12, 14, 15, 17, 18, 19, 21, 22, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41, 43, 45, 46, 47, 48, 49, 51, 52, 54, 56, 58, 59, 62, 63, 64, 65, 66, 67, 69, 70, 72, 73, 74, 75, 76, 78, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 93, 94, 95, 96, 97, 98, 99
Offset: 1

Views

Author

Vincenzo Librandi, Jun 25 2010

Keywords

Links

Crossrefs

Cf. A126424 (Numbers n for which n^4-n-1 is prime)

Programs

  • Magma
    [n: n in [2..100] |not IsPrime(n^4 - n - 1)]; // Vincenzo Librandi, Oct 15 2012
  • Mathematica
    Select[Range[2, 100], !PrimeQ[#^4 - # - 1] &] (* Vincenzo Librandi, Oct 15 2012 *)

A236766 Numbers n such that n^4 +/- n +/- 1 are prime for all four possibilities.

Original entry on oeis.org

6, 9, 7266, 115131, 380529, 536646, 636609, 818526, 922734, 1389015, 1660119, 2045415, 2085726, 2262420, 2469396, 2722260, 2836374, 2954250, 3146904, 3614226, 3949770, 4062465, 4110834, 4211499, 4400100, 5081055, 5324424, 5434794, 5436090
Offset: 1

Views

Author

Derek Orr, Jan 30 2014

Keywords

Examples

			380529^4+380529+1 (20967711831335262645811), 380529^4+380529-1 (20967711831335262645809), 380529^4-380529+1 (20967711831335261884753), and 380529^4-380529-1 (20967711831335261884751) are all prime. Thus, 380529 is a member of this sequence.

Crossrefs

Intersection of A236759, A049408, A236761 and A126424.

Programs

  • Mathematica
    Select[Range[55*10^5],AllTrue[#^4+{(#-1),(#+1),(-#-1),(-#+1)},PrimeQ]&] (* Harvey P. Dale, Nov 02 2024 *)
  • PARI
    for(n=1, 5000000, if(isprime(n^4+n+1)&&isprime(n^4-n+1)&&isprime(n^4+n-1)&&isprime(n^4-n-1), print1(n, ","))) \\ Colin Barker, Jan 31 2014
  • Python
    import sympy
from sympy import isprime
{print(n) for n in range(10**7) if isprime(n**4+n+1) and isprime(n**4-n+1) and isprime(n**4+n-1) and isprime(n**4-n-1)}
Previous Showing 11-17 of 17 results.

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

Content is available under The OEIS End-User License Agreement.