A268304 Odd numbers n such that binomial(6*n, 2*n) == -1 (mod 8).

1, 5, 21, 73, 85, 273, 293, 297, 329, 341, 529, 545, 1041, 1057, 1089, 1093, 1105, 1173, 1189, 1193, 1297, 1317, 1321, 1353, 1365, 2065, 2081, 2113, 2117, 2129, 2177, 2181, 2209, 2577, 2593, 4113, 4129, 4161, 4165, 4177, 4225, 4229, 4257, 4353, 4357, 4373, 4417, 4421, 4433

Offset

1,2

Comments

The primes p of this sequence are those that give the even semiprimes of A268303.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

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.

Mathematica

Select[Range[1, 5000, 2], Mod[Binomial[6 #, 2 #], 8] == 7 &] (* Michael De Vlieger, Feb 07 2016 *)

Prog

(PARI) isok(n) = (n%2) && Mod(binomial(6*n, 2*n), 8) == Mod(-1, 8);
(Python)
from __future__ import division
A268304_list, b, m1, m2 = [], 15, [21941965946880, -54854914867200, 49244258396160, -19011472727040, 2933960577120, -126898662960, 771887070, 385943535, 385945560],  [10569646080, -25763512320, 22419210240, -8309145600, 1209116160, -46992960, 415800, 311850, 311850]
for n in range(10**3):
    if b % 8 == 7:
        A268304_list.append(2*n+1)
    b = b*m1[-1]//m2[-1]
    for i in range(8):
        m1[i+1] += m1[i]
        m2[i+1] += m2[i] # Chai Wah Wu, Feb 05 2016

Crossrefs

Cf. A234839, A268303.

Sequence in context: A202462 A354701 A055280 * A273450 A186948 A271251

Adjacent sequences: A268301 A268302 A268303 * A268305 A268306 A268307

Keyword

nonn

Author

Michel Marcus, Jan 31 2016

Status

approved