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%I #14 Dec 13 2021 08:04:32
%S 83,173,197,269,317,389,461,557,653,701,797,941,1091,1109,1181,1229,
%T 1637,1709,1949,1997,2069,2141,2309,2531,2549,2621,2789,2861,3221,
%U 3389,3461,3581,3821,4157,4229,4349,4493,5051,5261,5381,5501,5693
%N Primes that can be written in the form 2*p^2 + 3*q^2 with p and q prime.
%C Subsequence of A084864 and of A084865; A084863(a(n))>0.
%H Robert Israel, <a href="/A084866/b084866.txt">Table of n, a(n) for n = 1..10000</a>
%e A000040(40) = 173 = 98 + 75 = 2*7^2 + 3*5^2 = 2*A000040(4)^2 + 3*A000040(3)^2, therefore 173 is a term.
%p N:= 10^4: # to get terms <= N
%p P:= select(isprime, [2,seq(i,i=3..floor((N/2)^(1/2)))]):
%p m:= nops(P):
%p R:= {}:
%p for p in P do
%p for i from 2 to m while 3*P[i]^2 <= N - 2*p^2 do
%p v:= 2*p^2 + 3*P[i]^2;
%p if isprime(v) then R:= R union {v} fi
%p od od:
%p sort(convert(R,list)); # _Robert Israel_, Nov 05 2020
%t nn = 10^4; (* to get terms <= nn *)
%t P = Select[Join[{2}, Range[3, Floor[Sqrt[nn/2]]]], PrimeQ];
%t m = Length[P];
%t R = {};
%t Do[For[i = 2, 3*P[[i]]^2 <= nn - 2*p^2, i++,
%t v = 2*p^2 + 3*P[[i]]^2;
%t If[PrimeQ[v], R = R ~Union~ {v}]],
%t {p, P}];
%t Sort[R] (* _Jean-François Alcover_, Dec 13 2021, after _Robert Israel_ *)
%Y Cf. A084863, A084864, A084865.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jun 10 2003
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