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A214723 Numbers of the form p^2 + q^2, with p and q prime, in exactly one way.

%I A214723 #26 Jul 13 2013 12:04:29
%S A214723 8,13,18,29,34,50,53,58,74,98,125,130,146,170,173,178,194,218,242,290,
%T A214723 293,298,314,365,370,386,458,482,530,533,538,554,698,722,818,845,850,
%U A214723 866,962,965,970,986,1058,1082,1202,1250,1322,1370,1373,1378,1394,1418
%N A214723 Numbers of the form p^2 + q^2, with p and q prime, in exactly one way.
%C A214723 A045698(a(n)) = 1. - _Reinhard Zumkeller_, Jul 29 2012
%H A214723 Reinhard Zumkeller, <a href="/A214723/b214723.txt">Table of n, a(n) for n = 1..1000</a>
%H A214723 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e A214723 a(1) = 8 = 2^2 + 2^2, and no other p^2 + q^2 sums to 8.
%e A214723 Both 7^2 + 17^2 and 13^2 + 13^2 sum to 338, so 338 is not in this sequence.
%t A214723 nn = 2000; ps = Prime[Range[PrimePi[Sqrt[nn]]]]; t = Flatten[Table[ps[[i]]^2 + ps[[j]]^2, {i, Length[ps]}, {j, i, Length[ps]}]]; t = Select[t, # <= nn &]; Sort[Transpose[Select[Tally[t], #[[2]] == 1 &]][[1]]] (* _T. D. Noe_, Jul 26 2012 *)
%o A214723 (Haskell)
%o A214723 import Data.List (elemIndices)
%o A214723 a214723 n = a214723_list !! (n-1)
%o A214723 a214723_list = elemIndices 1 a045698_list
%o A214723 -- _Reinhard Zumkeller_, Jul 29 2012
%Y A214723 Subsequence of A045636 (numbers of the form p^2 + q^2).
%K A214723 nonn
%O A214723 1,1
%A A214723 _J. Stauduhar_, Jul 26 2012