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A259142 Least prime p of the form n*q^2+(n+1)*r^2 with q and r prime.

%I A259142 #12 May 01 2018 02:44:52
%S A259142 17,83,43,61,149,199,263,113,331,139,383,373,173,191,199,569,587,547,
%T A259142 251,269,277,757,1223,1321,859,347,787,373,3779,1789,1063,953,433,
%U A259142 1181,1019,1069,1283,503,2311,5209,1193,1453,563,1301,2389,607,1367,1657,641,659,1483,1777,1811,1861,719,1913,1657,1997,4391,3229,797,1823
%N A259142 Least prime p of the form n*q^2+(n+1)*r^2 with q and r prime.
%C A259142 Values of {p,q,r}: {17,3,2},{83,2,5},{43,3,2},{61,2,3},{149,5,2},{199,2,5},{263,3,5},{113,2,3}.
%C A259142 a(2) = A084866(1). - _Michel Marcus_, Jun 20 2015
%C A259142 For p in A093191, a((p-4)/13) = p. - _Robert Israel_, Apr 30 2018
%H A259142 Robert Israel, <a href="/A259142/b259142.txt">Table of n, a(n) for n = 1..10000</a>
%H A259142 Zak Seidov, <a href="/A259142/a259142.txt">First 100 values of {p,q,r}.</a>
%e A259142 17=1*3^2+2*2^2, 83=2*2^2+3*5^2, 43=3*3^2+4*2^2.
%p A259142 P:= [seq(ithprime(i),i=1..20)]: np:= 20:
%p A259142 for n from 1 to 100 do
%p A259142   found:= false;
%p A259142   while not found do
%p A259142     R:= sort([seq(seq(n*q^2+(n+1)*p^2,p=P),q=P)]);
%p A259142     w:= n*4+(n+1)*P[-1]^2+1;
%p A259142     r:= ListTools:-SelectFirst(isprime,R);
%p A259142     if r <> NULL and r <= w then
%p A259142       A[n]:= r;
%p A259142       found:= true;
%p A259142     else
%p A259142       P:= [op(P), seq(ithprime(i),i=np+1..np+20)];
%p A259142       np:= np+20;
%p A259142     fi
%p A259142   od;
%p A259142 od:
%p A259142 seq(A[i],i=1..100); # _Robert Israel_, Apr 30 2018
%Y A259142 Cf. A000040, A093191.
%K A259142 nonn,look
%O A259142 1,1
%A A259142 _Zak Seidov_, Jun 19 2015