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%I #44 Sep 10 2019 21:47:22
%S 169,289,507,841,867,1183,1369,1521,1681,1859,2023,2523,2601,2809,
%T 3179,3211,3549,3721,3887,4107,4563,5043,5239,5329,5491,5577,5887,
%U 6069,6647,7267,7569,7803,7921,7943,8281,8427,8959,9251,9409,9537,9583,9633,9971
%N Numbers k coprime to 10 such that there are exactly two values of A for which k^2+4*A and k^2-4*A are perfect squares.
%C These are the odd integers k, not a multiple of 5, such that k^2 is an arithmetic mean of two other odd perfect squares in exactly two ways.
%e 169 is a term since 169^2±4*(5070) and 169^2±4*(7140) are all perfect squares.
%o (PARI) ok(k)={if(k%2==0||k%5==0, 0, my(k2=k^2, L=List()); forstep(i=1, k-1, 2, my(d=k2-i^2); if(issquare(k2+d), listput(L,i))); #L==2)}
%o for(k=1, 10000, if(ok(k), print1(k, ", "))) \\ _Andrew Howroyd_, Sep 06 2019
%Y Cf. A002144, A309812.
%K nonn
%O 1,1
%A _Mohsin A. Shaikh_, Sep 06 2019
%E a(28)-a(43) from _Andrew Howroyd_, Sep 06 2019
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