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%I A355518 #8 Jul 18 2022 19:37:47
%S A355518 2,3,5,13,17,37,61,137
%N A355518 Primes that cannot be represented as 2*p - q where p, q and 2*p^2 - q^2 are prime.
%C A355518 Conjecture: there are no other terms.
%e A355518 11 is not in the sequence because 11 = 2*7 - 3 with 7, 3 and 2*7^2 - 3^2 = 89 prime.
%p A355518 M:= 10000: # to get all terms <= M
%p A355518 Pmax:= floor(M/(2-sqrt(2))):
%p A355518 Qmax:= floor(sqrt(2)*Pmax):
%p A355518 Q:= select(isprime,[2,seq(i,i=3..Qmax,2)]):
%p A355518 P:= select(`<=`,Q,Pmax): nQ:= nops(Q):
%p A355518 S:= convert(select(`<=`,P,M),set):
%p A355518 for p in P  do
%p A355518   for j from 1 to nQ do
%p A355518     q:= Q[j];
%p A355518     r:= 2*p^2-q^2;
%p A355518     if r < 2 then break fi;
%p A355518     s:= 2*p-q;
%p A355518     if s <= M and isprime(r) and isprime(s) then S:= S minus {s} fi;
%p A355518 od od:
%p A355518 S;
%Y A355518 Cf. A355521.
%K A355518 nonn
%O A355518 1,1
%A A355518 _J. M. Bergot_ and _Robert Israel_, Jul 05 2022

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