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A226562 Numbers which are the sum of two squared primes in exactly three ways (ignoring order).

%I A226562 #29 Sep 20 2018 00:30:36
%S A226562 2210,3770,5330,6290,12818,16490,18122,19370,24050,24650,26690,32810,
%T A226562 33410,34970,36530,39650,39770,44642,45050,45890,49010,50690,51578,
%U A226562 57770,59450,61610,63050,66170,67490,72410,73610,74210,80330,85202,86210,86330,88010
%N A226562 Numbers which are the sum of two squared primes in exactly three ways (ignoring order).
%C A226562 Suggestion: difference between successive terms is always at least 3. (With the known 115885 terms <10^9, the smallest difference is 24.) - _Zak Seidov_, Jun 12 2013
%D A226562 Stan Wagon, Mathematica in Action, Springer, 2000 (2nd ed.), Ch. 17.5, pp. 375-378.
%H A226562 Zak Seidov, <a href="/A226562/b226562.txt">Table of n, a(n) for n = 1..2464</a> (all terms up to 10^7).
%e A226562 2210 = 19^2 + 43^2 = 23^2 + 41^2 = 29^2 + 37^2;
%p A226562 Prime2PairsSum := s -> select( x -> `if`(andmap(isprime, x), true, false), numtheory:-sum2sqr(s)):
%p A226562 for n from 2 to 10 do
%p A226562 if nops(Prime2PairsSum(n)) = 3 then print(n,Prime2PairsSum(n)) fi
%p A226562 od;
%t A226562 Select[Range@20000, Length[Select[ PowersRepresentations[#, 2, 2], And @@ PrimeQ[#] &]] == 3 &] (* _Giovanni Resta_, Jun 11 2013 *)
%Y A226562 Cf. A054735 (restricted to twin primes), A037073, A069496.
%Y A226562 Cf. A045636 (sum of two squared primes), A226539.
%Y A226562 Cf. A214511 (least number having n representations).
%Y A226562 Cf. A226539 (restricted to sums decomposed in exactly three ways).
%K A226562 nonn
%O A226562 1,1
%A A226562 _Henk Koppelaar_, Jun 11 2013
%E A226562 a(22)-a(37) from _Giovanni Resta_, Jun 11 2013