A242517 - OEIS

%I #24 Apr 06 2020 09:11:02

%S 31,619,2791,4801,15331,33829,40129,63421,69151,98731,127291,142789,

%T 143569,149971,151849,176599,184969,201829,210601,225289,231841,

%U 243589,250951,271279,273271,277549,280591,392269,405439,441799,472711,510709,530599,568441,578689

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

%H Amiram Eldar, <a href="/A242517/b242517.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..250 from Abhiram R Devesh)

%e 31 is in the sequence because

%e p = 31 (prime),

%e p - 2 = 29 (prime),

%e p^3 - 2 = 29789 (prime), and

%e p^5 - 2 = 28629149 (prime).

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

%o (Python)

%o import sympy

%o n=2

%o while n>1:

%o ....n1=n-2

%o ....n2=((n**3)-2)

%o ....n3=((n**5)-2)

%o ....##Check if n1, n2 and n3 are also primes.

%o ....if sympy.ntheory.isprime(n1)== True and sympy.ntheory.isprime(n2)== True and sympy.ntheory.isprime(n3)== True:

%o ........print(n, " , " , n1, " , ", n2, " , ", n3)

%o ....n=sympy.ntheory.nextprime(n)

%o (PARI) isok(p) = isprime(p) && isprime(p-2) && isprime(p^3-2) && isprime(p^5-2); \\ _Michel Marcus_, Apr 06 2020

%o (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

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

%Y Cf. A001359.

%K nonn,easy

%O 1,1

%A _Abhiram R Devesh_, May 17 2014