A348313 - OEIS

%I #11 Sep 22 2025 16:01:34

%S 5,11,13,71,73,97,149,223,229,283,337,353,401,409,577,827,887,1051,

%T 1277,1321,1489,1543,1627,1787,1931,2237,2467,2903,3137,3181,3559,

%U 3917,4243,4357,4363,4441,4583,4723,4933,5113,5693,5839,5857,6007,6043,6053,6121

%N Primes q such that q^3+r^5+s^7 is also prime, where q,r,s are consecutive primes.

%C Exponent values (3,5,7) given by the prime triplet of the form p, p+2, p+4.

%e 5 is a term because 5^3+7^5+11^7 = 19504103 is prime;

%e 11 is a term because 11^3+13^5+17^7 = 410711297 is prime.

%t Select[Partition[Select[Range[6000], PrimeQ], 3, 1], PrimeQ[#[[1]]^3 + #[[2]]^5 + #[[3]]^7] &][[;; , 1]] (* _Amiram Eldar_, Oct 11 2021 *)

%o (SageMath)

%o def Q(x):

%o     if Primes().unrank(x)^3+Primes().unrank(x+1)^5+Primes().unrank(x+2)^7 in Primes():

%o        return Primes().unrank(x)

%o A348313 = [Q(x) for x in range(0,10^3) if Q(x)!=None]

%o (PARI) isok(p) = if (isprime(p), my(q=nextprime(p+1), r=nextprime(q+1)); isprime(p^3+q^5+r^7)); \\ _Michel Marcus_, Oct 11 2021

%Y Cf. A000040, A348267.

%K nonn

%O 1,1

%A _Dumitru Damian_, Oct 11 2021