# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a268304 Showing 1-1 of 1 %I A268304 #11 Feb 07 2016 20:15:48 %S A268304 1,5,21,73,85,273,293,297,329,341,529,545,1041,1057,1089,1093,1105, %T A268304 1173,1189,1193,1297,1317,1321,1353,1365,2065,2081,2113,2117,2129, %U A268304 2177,2181,2209,2577,2593,4113,4129,4161,4165,4177,4225,4229,4257,4353,4357,4373,4417,4421,4433 %N A268304 Odd numbers n such that binomial(6*n, 2*n) == -1 (mod 8). %C A268304 The primes p of this sequence are those that give the even semiprimes of A268303. %H A268304 Chai Wah Wu, Table of n, a(n) for n = 1..10000 %H A268304 Marc Chamberland and Karl Dilcher, A Binomial Sum Related to Wolstenholme's Theorem, J. Number Theory, Vol. 171, Issue 11 (Nov. 2009), pp. 2659-2672. See Table 2 p. 2669. %t A268304 Select[Range[1, 5000, 2], Mod[Binomial[6 #, 2 #], 8] == 7 &] (* _Michael De Vlieger_, Feb 07 2016 *) %o A268304 (PARI) isok(n) = (n%2) && Mod(binomial(6*n, 2*n), 8) == Mod(-1, 8); %o A268304 (Python) %o A268304 from __future__ import division %o A268304 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 A268304 for n in range(10**3): %o A268304 if b % 8 == 7: %o A268304 A268304_list.append(2*n+1) %o A268304 b = b*m1[-1]//m2[-1] %o A268304 for i in range(8): %o A268304 m1[i+1] += m1[i] %o A268304 m2[i+1] += m2[i] # _Chai Wah Wu_, Feb 05 2016 %Y A268304 Cf. A234839, A268303. %K A268304 nonn %O A268304 1,2 %A A268304 _Michel Marcus_, Jan 31 2016 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE