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A226539 Numbers which are the sum of two squared primes in exactly two ways (ignoring order).

%I A226539 #29 Dec 15 2019 11:34:11
%S A226539 338,410,578,650,890,1010,1130,1490,1730,1802,1898,1970,2330,2378,
%T A226539 2738,3050,3170,3530,3650,3842,3890,4010,4658,4850,5018,5090,5162,
%U A226539 5402,5450,5570,5618,5690,5858,6170,6410,6530,6698,7010,7178,7202,7250,7850,7970,8090
%N A226539 Numbers which are the sum of two squared primes in exactly two ways (ignoring order).
%D A226539 Stan Wagon, Mathematica in Action, Springer, 2000 (2nd ed.), Ch. 17.5, pp. 375-378.
%H A226539 T. D. Noe, <a href="/A226539/b226539.txt">Table of n, a(n) for n = 1..10000</a>
%e A226539 338 = 7^2 + 17^2 = 13^2 + 13^2;
%e A226539 410 = 7^2 + 19^2 = 11^2 + 17^2.
%p A226539 Prime2PairsSum := p -> select(x ->`if`(andmap(isprime, x),true,false), numtheory:-sum2sqr(p)):
%p A226539 for n from 2 to 10^6 do
%p A226539   if nops(Prime2PairsSum(n)) = 2 then print(n, Prime2PairsSum(n)) fi;
%p A226539 od;
%t A226539 Select[Range@10000, Length[Select[ PowersRepresentations[#, 2, 2], And @@ PrimeQ[#] &]] == 2 &] (* _Giovanni Resta_, Jun 11 2013 *)
%o A226539 (PARI) select( is_A226539(n)={#[0|t<-sum2sqr(n),isprime(t[1])&&isprime(t[2])]==2}, [1..10^4]) \\ For more efficiency, apply selection to A045636. See A133388 for sum2sqr(). - _M. F. Hasler_, Dec 12 2019
%Y A226539 Cf. A054735 (restricted to twin primes), A037073, A069496.
%Y A226539 Cf. A045636 (sum of two squared primes: a superset).
%Y A226539 Cf. A214511 (least number having n representations).
%Y A226539 Cf. A226562 (restricted to sums decomposed in exactly three ways).
%K A226539 nonn
%O A226539 1,1
%A A226539 _Henk Koppelaar_, Jun 10 2013
%E A226539 a(25)-a(44) from _Giovanni Resta_, Jun 11 2013