A236761 -id:A236761 - cp's OEIS frontend

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

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

Derek Orr, Jan 30 2014

nonn

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

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

Intersection of A236761 and A126424.

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

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

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)}

A236940 Primes p such that p^4-p+1 is prime.

Original entry on oeis.org

3, 13, 19, 43, 79, 109, 313, 379, 613, 709, 1171, 1213, 1399, 1543, 1693, 1759, 1861, 1933, 2089, 2239, 2341, 2371, 2503, 2521, 2731, 2749, 3001, 3061, 3229, 3433, 3571, 3739, 3769, 4219, 4801, 4933, 4951, 4993, 5011, 5023, 5209, 5281

Offset: 1

Derek Orr, Feb 01 2014

nonn

Primes in the sequence A236761.

			1213 is prime and 1213^4 - 1213 + 1 = 2164926732949 is prime. Thus, 1213 is a member of this sequence.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A236761.

[p: p in PrimesUpTo(6000) | IsPrime(p^4-p+1)]; // Vincenzo Librandi, Feb 14 2014

Select[Prime[Range[10000]], PrimeQ[#^4 - # + 1]&] (* Vincenzo Librandi, Feb 14 2014 *)

s=[]; forprime(p=2, 6000, if(isprime(p^4-p+1), s=concat(s, p))); s \\ Colin Barker, Feb 05 2014

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

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

Derek Orr, Jan 30 2014

nonn

			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.

Intersection of A236759, A049408, A236761 and A126424.

Select[Range[55*10^5],AllTrue[#^4+{(#-1),(#+1),(-#-1),(-#+1)},PrimeQ]&] (* Harvey P. Dale, Nov 02 2024 *)

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

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)}

cp's OEIS Frontend

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

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A236940 Primes p such that p^4-p+1 is prime.

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Magma

Mathematica

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

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Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Python