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A348267 Primes of the form q^3+r^5+s^7, where q,r,s are consecutive primes.

%I A348267 #21 Nov 11 2021 21:07:26
%S A348267 19504103,410711297,895293793,19205982415663,27139128435043,
%T A348267 122997897555661,2351321783571193,33026024797765183,44544286011297461,
%U A348267 257023170905666323,630639912549644209,896737512757442999,2267254920439040789,2344105012311523369,25786002910400593997
%N A348267 Primes of the form q^3+r^5+s^7, where q,r,s are consecutive primes.
%C A348267 Exponent values (3,5,7) given by the prime triplet of the form p,p+2,p+4.
%e A348267 19504103 is a term because 5^3+7^5+11^7 = 19504103 is prime;
%e A348267 410711297 is a term because 11^3+13^5+17^7 = 410711297 is prime.
%t A348267 Select[(#[[1]]^3 + #[[2]]^5 + #[[3]]^7) & /@ Partition[Select[Range[1000], PrimeQ], 3, 1], PrimeQ] (* _Amiram Eldar_, Oct 11 2021 *)
%o A348267 (Sage)
%o A348267 def Q3R5S7(x):
%o A348267     return Primes().unrank(x)^3+Primes().unrank(x+1)^5+Primes().unrank(x+2)^7
%o A348267 A348267 = [Q3R5S7(x) for x in range(0,10^3) if Q3R5S7(x) in Primes()]
%Y A348267 Cf. A000040, A348313, A259772, A304292.
%K A348267 nonn
%O A348267 1,1
%A A348267 _Dumitru Damian_, Oct 09 2021