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%I #14 Mar 03 2017 20:53:16
%S 1,3,87,195,243,297,408,495,522,528,573,600,798,885,903,957,1038,1053,
%T 1110,1200,1233,1293,1302,1308,1368,1473,1482,1578,1623,1797,1953,
%U 2028,2142,2238,2370,2772,2868,2973,3033,3393,3483,3582,3777,3822,3840,3912
%N Numbers n with (p,p+2) = ((2*n)^3/2 - 1,(2*n)^3/2 + 1) is a twin prime pair.
%C For k > 1: n = a(k) is necessarily a multiple of 3.
%H Harvey P. Dale, <a href="/A172494/b172494.txt">Table of n, a(n) for n = 1..1000</a>
%F 2*a(n) = (2*A172271(n) + 2)^(1/3). - _R. J. Mathar_, Aug 21 2014
%e 3 = (2*1)^3/2 - 1 = prime(2), 3 + 2 = 5 = (2*1)^3/2 + 1, (3,5) is the first twin prime pair => a(1) = 1.
%e 107 = (2*3)^3/2 - 1 = prime(28), 107 + 2 = 109 = (2*3)^3/2 + 1, (107,109) is the 10th twin prime pair => a(2) = 3.
%t Select[Range[4000],AllTrue[(2#)^3/2+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jan 21 2015 *)
%o (PARI)
%o select(n -> isprime((2*n)^3/2-1) && isprime((2*n)^3/2+1), [1..4000]) \\ _Satish Bysany_, Mar 03 2017
%Y Cf. A172271, A001359, A061308, A069496, A061308, A119859.
%K nonn
%O 1,2
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), Feb 05 2010
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