A243900 - OEIS

%I #14 Jan 16 2018 02:45:45

%S 3,5,19,23,277,751,1549,2851,2963,3089,3463,3511,4057,6067,6619,7873,

%T 9257,10937,11161,11321,11483,12589,13997,15139,25121,25939,26113,

%U 26861,30971,33889,37139,38119,39251,39979,40763,41851,42359,44293,50753,50867,51907,54331,54401,55871,56921,58321,60611,62459

%N Prime p such that p^5 + p^3 + p - 4 and p^5 + p^3 + p + 4 are primes.

%C Intersection of A243898 (Prime p such that p^5 + p^3 + p + 4 is prime) and A243899 (Prime p such that p^5 + p^3 + p - 4 is prime).

%H Abhiram R Devesh, <a href="/A243900/b243900.txt">Table of n, a(n) for n = 1..1000</a>

%e Prime p = 3 is in this sequence as p^5 + p^3 + p + 4 = 277 (prime) and p^5 + p^3 + p - 4 = 269 (prime).

%e Prime p = 5 is in this sequence as p^5 + p^3 + p + 4 = 3259 (prime) and p^5 + p^3 + p - 4 = 3251 (prime).

%t Select[Prime@ Range[10^4], AllTrue[#^5 + #^3 + # + {-4, 4}, PrimeQ] &] (* _Michael De Vlieger_, Jan 15 2018 *)

%o (Python)

%o import sympy.ntheory as snt

%o p=1

%o while p>0:

%o ....p=snt.nextprime(p)

%o ....pp=p+(p**3)+(p**5)-4

%o ....qq=p+(p**3)+(p**5)+4

%o ....if snt.isprime(pp) == True and snt.isprime(qq) == True:

%o ........print(p)

%Y Cf. A243898, A243899.

%K nonn

%O 1,1

%A _Abhiram R Devesh_, Jun 14 2014