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%I #4 Jul 13 2022 07:20:10
%S 2,3,5,7,13,31,37,97,211,271
%N Primes that cannot be represented as 2*p+q where p, q and (2*p^2+q^2)/3 are prime.
%C 2*p^2+q^2 is always divisible by 3 when neither p nor q is divisible by 3.
%C Conjecture: there are no other terms.
%e 11 is not in the sequence because 11 = 2*2+7 with 2, 7 and (2*2^2+7^2)/3 = 19 prime.
%p M:= 50000:
%p Pr:= select(isprime, [2,seq(i,i=5..M,2)]):
%p nP:= nops(Pr):
%p S:= convert(Pr,set) union {3}:
%p for p in Pr do
%p if 2*p+2 > M then break fi;
%p for q in Pr do
%p r:= 2*p+q;
%p if r > M then break fi;
%p if isprime(r) and isprime((2*p^2+q^2)/3) then
%p S:= S minus {r}
%p fi
%p od od:
%p S;
%Y Cf. A355518.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Jul 05 2022
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