A126421 -id:A126421 - cp's OEIS frontend

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

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

Offset: 1

Artur Jasinski, Dec 26 2006

nonn

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

map(t -> t^7-t-1, select(t -> isprime(t^7-t-1), [$1..10^4])); # Robert Israel, Jul 22 2019

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

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, A126427, A126428, A126429, A126430, A126431, A126432 A126433, A126434, A126434.

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 *)

A158295 Primes p such that p^3-p-+1 are twin primes.

Original entry on oeis.org

2, 11, 31, 41, 239, 521, 2309, 4099, 4409, 4441, 4651, 5009, 5039, 5261, 6481, 6871, 7129, 8609, 9391, 10259, 12841, 13759, 14519, 14879, 14939, 15569, 16871, 18451, 20369, 22441, 24049, 25841, 28151, 28279, 29429, 30181, 30631, 32089, 32299, 36781

Offset: 1

Vladimir Joseph Stephan Orlovsky, Mar 15 2009

nonn

Primes p such that p^3+p-+1 are twin primes, so far only one: 3. 3^3+3=30-+1 = primes.

Primes in the sequence A236524. Odd primes are congruent to either 1 mod 10 or 9 mod 10. - Derek Orr, Jan 27 2014

			2^3-2=6-+1 = 5,7 primes, 11^3-11-+1 = 1319,1321 primes...

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A120364, A088483, A236524, A236477, A126421.

lst={};Do[p=Prime[n];a=p^3-p;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p]],{n,8!}];lst
Select[Prime[Range[3500]],And@@PrimeQ[#^3-#+{1,-1}]&] (* Harvey P. Dale, Jan 05 2013 *)

s=[]; forprime(p=2, 40000, if(isprime(p^3-p-1) && isprime(p^3-p+1), s=concat(s, p))); s /* Colin Barker, Jan 28 2014 */

import sympy
from sympy import isprime
{print(p) for p in range(10**5) if isprime(p) and isprime(p**3-p-1) and isprime(p**3-p+1)} # Derek Orr, Jan 27 2014

A236524 Numbers n such that n^3 - n +/- 1 are twin primes.

Original entry on oeis.org

2, 4, 11, 14, 15, 21, 31, 35, 41, 45, 111, 130, 136, 140, 155, 176, 189, 221, 230, 239, 274, 316, 406, 414, 441, 465, 466, 504, 521, 561, 570, 580, 584, 591, 686, 689, 696, 759, 834, 836, 860, 869, 904, 960, 1026, 1159, 1379, 1539, 1614, 1625, 1660

Offset: 1

Derek Orr, Jan 27 2014

nonn

			561^3 - 561 + 1 (176557921) and 561^3 - 561 - 1 (176557919) are twin primes. Thus, 561 is a member of this sequence.

Vincenzo Librandi, Table of n, a(n) for n = 1..2600

Intersection of A126421 and A236477.

[n: n in [1..2000] | IsPrime(n^3-n-1) and IsPrime(n^3-n+1)]; // Vincenzo Librandi, Jan 30 2018

Select[Range[2000], PrimeQ[#^3 - # - 1] && PrimeQ[#^3 - # + 1] &] (* Vincenzo Librandi, Jan 30 2018 *)

import sympy
from sympy import isprime
{print(n) for n in range(10**4) if isprime(n**3-n-1) and isprime(n**3-n+1)}

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

Artur Jasinski, Dec 26 2006

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

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 *)

A236168 Primes p such that p^3 - p - 1 is prime.

Original entry on oeis.org

2, 3, 11, 23, 29, 31, 41, 59, 71, 113, 151, 163, 191, 239, 241, 269, 359, 431, 433, 499, 503, 521, 541, 563, 661, 683, 701, 751, 773, 829, 883, 983, 1039, 1259, 1483, 1499, 1511, 1549, 1571, 1609, 1693, 1721, 1759, 1913

Offset: 1

Derek Orr, Jan 19 2014

nonn

Primes in A126421.

			269 is prime and 269^3 - 269 - 1 is also prime. So, 269 is a member of this sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A126421.

Select[Prime[Range[300]],PrimeQ[#^3-#-1]&] (* Harvey P. Dale, Nov 17 2014 *)

s=[]; forprime(p=2, 2000, if(isprime(p^3-p-1), s=concat(s, p))); s \\ Colin Barker, Jan 20 2014

import sympy
from sympy import isprime
{print(p) for p in range(10**4) if isprime(p) and isprime(p**3-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

Derek Orr, Jan 19 2014

nonn

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

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

Cf. A002328, A126421, A126424.

Select[Range[15000], And @@ PrimeQ[#^Range[2, 4] - # - 1] &] (* Amiram Eldar, Mar 21 2020 *)

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

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)}

A236764 Numbers k such that k^3 +/- k +/- 1 are prime for all four possibilities.

Original entry on oeis.org

15, 21, 15375, 25164, 53361, 95190, 110685, 115140, 133701, 139425, 140430, 140844, 189336, 217686, 220650, 266916, 272469, 289341, 344880, 364665, 377805, 382221, 390270, 415779, 454905, 539700, 561186, 567645, 575799, 584430, 603651, 722484

Offset: 1

Derek Orr, Jan 30 2014

nonn

			110685^3+110685+1 (1356020665779811), 110685^3+110685-1 (1356020665779809), 110685^3-110685+1 (1356020665558441) and 110685^3-110685-1 (1356020665558439) are all prime. Thus 110685 is a member of this sequence.

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

Intersection of A126421, A236477, A049407, and A236475.

for(n=1, 800000, if(isprime(n^3+n+1)&&isprime(n^3-n+1)&&isprime(n^3+n-1)&&isprime(n^3-n-1), print1(n, ","))) \\ Colin Barker, Jan 31 2014

import sympy
from sympy import isprime
{print(n) for n in range(10**6) if isprime(n**3+n+1) and isprime(n**3-n+1) and isprime(n**3+n-1) and isprime(n**3-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

Artur Jasinski, Dec 26 2006, Jan 19 2007

nonn

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

a = {}; Do[k = 2; While[ ! PrimeQ[k^n -k - 1], k++ ]; AppendTo[a, k^n - k - 1], {n, 2, 30}]; a (*Artur Jasinski*)

A177089 Numbers n >= 0 such that n^3-n-1 is not prime.

Original entry on oeis.org

0, 1, 5, 6, 7, 10, 12, 13, 17, 19, 20, 22, 25, 26, 27, 28, 30, 32, 33, 34, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 52, 53, 54, 56, 57, 61, 62, 63, 65, 66, 67, 68, 72, 73, 74, 75, 77, 78, 79, 80, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102

Offset: 1

Vincenzo Librandi, Jun 05 2010

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A126421.

remove(n -> isprime(n^3-n-1), [$0..1000]); # Robert Israel, Jul 14 2017

isok(n) = !isprime(n^3-n-1); \\ Michel Marcus, Jul 14 2017

Checked by Jud McCranie, Jun 16 2010

0 and 1 added by R. J. Mathar, Jun 18 2010

cp's OEIS Frontend

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

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

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A158295 Primes p such that p^3-p-+1 are twin primes.

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A236524 Numbers n such that n^3 - n +/- 1 are twin primes.

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Magma

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

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A236168 Primes p such that p^3 - p - 1 is prime.

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

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Mathematica

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A236764 Numbers k such that k^3 +/- k +/- 1 are prime for all four possibilities.

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