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Integers n such that n^2 = 2*x*(y-x), where x and y are consecutive terms in A014574.
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%I #31 Apr 02 2015 05:25:44

%S 4,12,48,120,468,1260,720,2448,10080,12060,15912,7560,18480,7392,9660,

%T 27720,33480,14400,25080,36708,10092,34188,42120,83400,29820,20040,

%U 67320,114408,206628,67368,72192,102648,152928,51732,59880,152700,106440,100980,171480

%N Integers n such that n^2 = 2*x*(y-x), where x and y are consecutive terms in A014574.

%C n is a term if n^2 = 2*x*(y-x), where x and y are the averages of two consecutive twin prime pairs.

%e 48^2 = 2*192*(198-192), and 192 and 198 are consecutive terms in A014574, so 48 is in the sequence.

%o (PARI) lista(nn) = {p=2; last = 0; forprime (q=3, nn, if (q-p==2, if (! last, last = p+1, new = p+1; val = new^2-last^2 - (new-last)^2; if (issquare(val), print1(sqrtint(val), ", ")); last = new; );); p=q;);} \\ _Michel Marcus_, Feb 18 2015

%Y Cf. A014574.

%K nonn

%O 1,1

%A _Neri Gionata_, Feb 18 2015

%E More terms from _Michel Marcus_, Feb 18 2015