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A348313 Primes q such that q^3+r^5+s^7 is also prime, where q,r,s are consecutive primes.

%I A348313 #10 Nov 11 2021 21:06:57
%S A348313 5,11,13,71,73,97,149,223,229,283,337,353,401,409,577,827,887,1051,
%T A348313 1277,1321,1489,1543,1627,1787,1931,2237,2467,2903,3137,3181,3559,
%U A348313 3917,4243,4357,4363,4441,4583,4723,4933,5113,5693,5839,5857,6007,6043,6053,6121
%N A348313 Primes q such that q^3+r^5+s^7 is also prime, where q,r,s are consecutive primes.
%C A348313 Exponent values (3,5,7) given by the prime triplet of the form p, p+2, p+4.
%e A348313 5 is a term because 5^3+7^5+11^7 = 19504103 is prime;
%e A348313 11 is a term because 11^3+13^5+17^7 = 410711297 is prime.
%t A348313 Select[Partition[Select[Range[6000], PrimeQ], 3, 1], PrimeQ[#[[1]]^3 + #[[2]]^5 + #[[3]]^7] &][[;; , 1]] (* _Amiram Eldar_, Oct 11 2021 *)
%o A348313 (Sage)
%o A348313 def Q(x):
%o A348313     if Primes().unrank(x)^3+Primes().unrank(x+1)^5+Primes().unrank(x+2)^7 in Primes():
%o A348313        return Primes().unrank(x)
%o A348313 A348313 = [Q(x) for x in range(0,10^3) if Q(x)!=None]
%o A348313 (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 A348313 Cf. A000040, A348267.
%K A348313 nonn
%O A348313 1,1
%A A348313 _Dumitru Damian_, Oct 11 2021