A242517 List of primes p for which p^n - 2 is prime for n = 1, 3, and 5.

31, 619, 2791, 4801, 15331, 33829, 40129, 63421, 69151, 98731, 127291, 142789, 143569, 149971, 151849, 176599, 184969, 201829, 210601, 225289, 231841, 243589, 250951, 271279, 273271, 277549, 280591, 392269, 405439, 441799, 472711, 510709, 530599, 568441, 578689

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..250 from Abhiram R Devesh)

Example

31 is in the sequence because
p = 31 (prime),
p - 2 = 29 (prime),
p^3 - 2 = 29789 (prime), and
p^5 - 2 = 28629149 (prime).

Mathematica

Select[Range[600000], PrimeQ[#] && AllTrue[#^{1, 3, 5} - 2, PrimeQ] &] (* Amiram Eldar, Apr 06 2020 *)

Prog

(Python)
import sympy
n=2
while n>1:
....n1=n-2
....n2=((n**3)-2)
....n3=((n**5)-2)
....##Check if n1, n2 and n3 are also primes.
....if sympy.ntheory.isprime(n1)== True and sympy.ntheory.isprime(n2)== True and sympy.ntheory.isprime(n3)== True:
........print(n, " , " , n1, " , ", n2, " , ", n3)
....n=sympy.ntheory.nextprime(n)
(PARI) isok(p) = isprime(p) && isprime(p-2) && isprime(p^3-2) && isprime(p^5-2); \\ Michel Marcus, Apr 06 2020
(PARI) list(lim)=my(v=List(), p=29); forprime(q=31, lim, if(q-p==2 && isprime(q^3-2) && isprime(q^5-2), listput(v, q)); p=q); Vec(v) \\ Charles R Greathouse IV, Apr 06 2020

Crossrefs

Intersection of A006512, A178251 and A154834, hence, intersection of A240126 and A154834.

Cf. A001359.

Sequence in context: A028142 A028148 A028100 * A028141 A302857 A028096

Adjacent sequences: A242514 A242515 A242516 * A242518 A242519 A242520

Keyword

nonn,easy

Author

Abhiram R Devesh, May 17 2014

Status

approved