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%I #11 Feb 07 2016 20:15:48
%S 1,5,21,73,85,273,293,297,329,341,529,545,1041,1057,1089,1093,1105,
%T 1173,1189,1193,1297,1317,1321,1353,1365,2065,2081,2113,2117,2129,
%U 2177,2181,2209,2577,2593,4113,4129,4161,4165,4177,4225,4229,4257,4353,4357,4373,4417,4421,4433
%N Odd numbers n such that binomial(6*n, 2*n) == -1 (mod 8).
%C The primes p of this sequence are those that give the even semiprimes of A268303.
%H Chai Wah Wu, <a href="/A268304/b268304.txt">Table of n, a(n) for n = 1..10000</a>
%H Marc Chamberland and Karl Dilcher, <a href="http://dx.doi.org/10.1016/j.jnt.2009.05.010">A Binomial Sum Related to Wolstenholme's Theorem</a>, J. Number Theory, Vol. 171, Issue 11 (Nov. 2009), pp. 2659-2672. See Table 2 p. 2669.
%t Select[Range[1, 5000, 2], Mod[Binomial[6 #, 2 #], 8] == 7 &] (* _Michael De Vlieger_, Feb 07 2016 *)
%o (PARI) isok(n) = (n%2) && Mod(binomial(6*n, 2*n), 8) == Mod(-1, 8);
%o (Python)
%o from __future__ import division
%o A268304_list, b, m1, m2 = [], 15, [21941965946880, -54854914867200, 49244258396160, -19011472727040, 2933960577120, -126898662960, 771887070, 385943535, 385945560], [10569646080, -25763512320, 22419210240, -8309145600, 1209116160, -46992960, 415800, 311850, 311850]
%o for n in range(10**3):
%o if b % 8 == 7:
%o A268304_list.append(2*n+1)
%o b = b*m1[-1]//m2[-1]
%o for i in range(8):
%o m1[i+1] += m1[i]
%o m2[i+1] += m2[i] # _Chai Wah Wu_, Feb 05 2016
%Y Cf. A234839, A268303.
%K nonn
%O 1,2
%A _Michel Marcus_, Jan 31 2016