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%I #11 Mar 16 2016 16:58:37
%S 3,179,521,809,1619,1871,2087,2339,3257,3329,4049,4337,4931,5651,5849,
%T 6569,6659,6947,7487,8009,8387,8819,8999,10529,10889,11699,12239,
%U 14561,15137,16361,16451,16649,17657,17747,19079,19889,19961,20231,20771,20807,21059,22481,22697,23039,23201
%N Lesser of twin primes such that sum of twin prime pair is the sum of 2 nonzero squares.
%e 3 is a term because 3 + 5 = 2^2 + 2^2.
%e 179 is a term because 179 + 181 = 6^2 + 18^2.
%e 521 is a term because 521 + 523 = 12^2 + 30^2.
%e 809 is a term because 809 + 811 = 18^2 + 36^2.
%t Select[Select[Prime@ Range@ 2700, PrimeQ[# + 2] &], Length[PowersRepresentations[2 # + 2, 2, 2] /. {0, _} -> Nothing] > 0 &] (* _Michael De Vlieger_, Mar 15 2016 *)
%o (PARI) isA000404(n)={ for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))}
%o t(n,p=3) = {while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
%o for(n=1, 1e3, if(isA000404(2*t(n)+2), print1(t(n), ", ")));
%Y Cf. A000404, A001359, A054735.
%K nonn
%O 1,1
%A _Altug Alkan_, Mar 13 2016
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