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%I #23 Aug 26 2014 09:41:44
%S 17,19,71,73,881,883,1151,1153,2591,2593,3527,3529,4049,4051,15137,
%T 15139,20807,20809,34847,34849,46817,46819,69191,69193,83231,83233,
%U 103967,103969,112337,112339,149057,149059,176417,176419,179999,180001,206081,206083
%N Twin prime pairs which sum to perfect squares.
%C All square roots of twin prime sums in this sequence (see A152786) are multiples of 6.
%C Digital roots of all pairs in this sequence are {8,1}.
%C Twin primes of the form 18n^2 +- 1. - _Charles R Greathouse IV_, Aug 26 2014
%H T. D. Noe, <a href="/A232878/b232878.txt">Table of n, a(n) for n = 1..10000</a>
%H Gary W. Croft, <a href="http://www.primesdemystified.com/Perfect_Twin_Primes.jpg">Perfect Twin Primes</a>
%F a(2n)=a(2n-1)+2. a(2n+1)=A069496(n).
%e 17+19 = 36, square root of 36 = 6; 71+73 = 144, square root of 144 = 12.
%t t = {}; Do[ps = {2 n^2 - 1, 2 n^2 + 1}; If[PrimeQ[ps[[1]]] && PrimeQ[ps[[2]]], AppendTo[t, ps]], {n, 1000}]; Flatten[t] (* _T. D. Noe_, Dec 03 2013 *)
%o (PARI) for(n=1,1e3, if(isprime(t=18*n^2-1) && isprime(t+2), print1(t", "t+2", "))) \\ _Charles R Greathouse IV_, Aug 26 2014
%Y Cf. A001097, A054735, A069496, A077800.
%K nonn
%O 1,1
%A _Gary Croft_, Dec 01 2013
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